Matematika Berhingga Contoh

$[\begin{array}{c} - 6 & 8 & 2 & 4 & - 3 \\ 1 & 9 & 7 & - 12 & 5 \\ 15 & 2 & - 8 & 10 & 11 \\ 4 & 7 & 9 & 6 & - 2 \\ 1 & 3 & 8 & 23 & 4 \end{array}] [\begin{array}{c} 5 & - 3 & 7 & 9 & 2 \\ 6 & 8 & - 5 & 2 & 1 \\ 3 & 7 & - 4 & 2 & 11 \\ 5 & - 3 & 9 & 4 & - 1 \\ 0 & 3 & 2 & 5 & 1 \end{array}]$

Langkah 1

Kalikan $[\begin{array}{c} - 6 & 8 & 2 & 4 & - 3 \\ 1 & 9 & 7 & - 12 & 5 \\ 15 & 2 & - 8 & 10 & 11 \\ 4 & 7 & 9 & 6 & - 2 \\ 1 & 3 & 8 & 23 & 4 \end{array}] [\begin{array}{c} 5 & - 3 & 7 & 9 & 2 \\ 6 & 8 & - 5 & 2 & 1 \\ 3 & 7 & - 4 & 2 & 11 \\ 5 & - 3 & 9 & 4 & - 1 \\ 0 & 3 & 2 & 5 & 1 \end{array}]$ .

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Langkah 1.1

Two matrices can be multiplied if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. In this case, the first matrix is $5 \times 5$ and the second matrix is $5 \times 5$ .

Langkah 1.2

Kalikan setiap baris pada matriks pertama dengan setiap kolom pada matriks kedua.

$[\begin{array}{c} - 6 \cdot 5 + 8 \cdot 6 + 2 \cdot 3 + 4 \cdot 5 - 3 \cdot 0 & - 6 \cdot - 3 + 8 \cdot 8 + 2 \cdot 7 + 4 \cdot - 3 - 3 \cdot 3 & - 6 \cdot 7 + 8 \cdot - 5 + 2 \cdot - 4 + 4 \cdot 9 - 3 \cdot 2 & - 6 \cdot 9 + 8 \cdot 2 + 2 \cdot 2 + 4 \cdot 4 - 3 \cdot 5 & - 6 \cdot 2 + 8 \cdot 1 + 2 \cdot 11 + 4 \cdot - 1 - 3 \cdot 1 \\ 1 \cdot 5 + 9 \cdot 6 + 7 \cdot 3 - 12 \cdot 5 + 5 \cdot 0 & 1 \cdot - 3 + 9 \cdot 8 + 7 \cdot 7 - 12 \cdot - 3 + 5 \cdot 3 & 1 \cdot 7 + 9 \cdot - 5 + 7 \cdot - 4 - 12 \cdot 9 + 5 \cdot 2 & 1 \cdot 9 + 9 \cdot 2 + 7 \cdot 2 - 12 \cdot 4 + 5 \cdot 5 & 1 \cdot 2 + 9 \cdot 1 + 7 \cdot 11 - 12 \cdot - 1 + 5 \cdot 1 \\ 15 \cdot 5 + 2 \cdot 6 - 8 \cdot 3 + 10 \cdot 5 + 11 \cdot 0 & 15 \cdot - 3 + 2 \cdot 8 - 8 \cdot 7 + 10 \cdot - 3 + 11 \cdot 3 & 15 \cdot 7 + 2 \cdot - 5 - 8 \cdot - 4 + 10 \cdot 9 + 11 \cdot 2 & 15 \cdot 9 + 2 \cdot 2 - 8 \cdot 2 + 10 \cdot 4 + 11 \cdot 5 & 15 \cdot 2 + 2 \cdot 1 - 8 \cdot 11 + 10 \cdot - 1 + 11 \cdot 1 \\ 4 \cdot 5 + 7 \cdot 6 + 9 \cdot 3 + 6 \cdot 5 - 2 \cdot 0 & 4 \cdot - 3 + 7 \cdot 8 + 9 \cdot 7 + 6 \cdot - 3 - 2 \cdot 3 & 4 \cdot 7 + 7 \cdot - 5 + 9 \cdot - 4 + 6 \cdot 9 - 2 \cdot 2 & 4 \cdot 9 + 7 \cdot 2 + 9 \cdot 2 + 6 \cdot 4 - 2 \cdot 5 & 4 \cdot 2 + 7 \cdot 1 + 9 \cdot 11 + 6 \cdot - 1 - 2 \cdot 1 \\ 1 \cdot 5 + 3 \cdot 6 + 8 \cdot 3 + 23 \cdot 5 + 4 \cdot 0 & 1 \cdot - 3 + 3 \cdot 8 + 8 \cdot 7 + 23 \cdot - 3 + 4 \cdot 3 & 1 \cdot 7 + 3 \cdot - 5 + 8 \cdot - 4 + 23 \cdot 9 + 4 \cdot 2 & 1 \cdot 9 + 3 \cdot 2 + 8 \cdot 2 + 23 \cdot 4 + 4 \cdot 5 & 1 \cdot 2 + 3 \cdot 1 + 8 \cdot 11 + 23 \cdot - 1 + 4 \cdot 1 \end{array}]$

Langkah 1.3

Sederhanakan setiap elemen dalam matriks dengan mengalikan semua pernyataannya.

$[\begin{array}{c} 44 & 75 & - 60 & - 33 & 11 \\ 20 & 169 & - 164 & 18 & 105 \\ 113 & - 82 & 239 & 218 & - 55 \\ 119 & 83 & 7 & 82 & 106 \\ 162 & 20 & 175 & 143 & 74 \end{array}]$

Langkah 2

Find the determinant.

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Langkah 2.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + & - & + \\ - & + & - & + & - \\ + & - & + & - & + \\ - & + & - & + & - \\ + & - & + & - & + \end{array} |$

Langkah 2.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 169 & - 164 & 18 & 105 \\ - 82 & 239 & 218 & - 55 \\ 83 & 7 & 82 & 106 \\ 20 & 175 & 143 & 74 \end{array} |$

Langkah 2.1.4

Multiply element $a_{11}$ by its cofactor.

$44 | \begin{array}{c} 169 & - 164 & 18 & 105 \\ - 82 & 239 & 218 & - 55 \\ 83 & 7 & 82 & 106 \\ 20 & 175 & 143 & 74 \end{array} |$

Langkah 2.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} |$

Langkah 2.1.6

Multiply element $a_{12}$ by its cofactor.

$- 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} |$

Langkah 2.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} |$

Langkah 2.1.8

Multiply element $a_{13}$ by its cofactor.

$- 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} |$

Langkah 2.1.9

The minor for $a_{14}$ is the determinant with row $1$ and column $4$ deleted.

$| \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} |$

Langkah 2.1.10

Multiply element $a_{14}$ by its cofactor.

$33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} |$

Langkah 2.1.11

The minor for $a_{15}$ is the determinant with row $1$ and column $5$ deleted.

$| \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.1.12

Multiply element $a_{15}$ by its cofactor.

$11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.1.13

Add the terms together.

$44 | \begin{array}{c} 169 & - 164 & 18 & 105 \\ - 82 & 239 & 218 & - 55 \\ 83 & 7 & 82 & 106 \\ 20 & 175 & 143 & 74 \end{array} | - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2

Evaluasi $| \begin{array}{c} 169 & - 164 & 18 & 105 \\ - 82 & 239 & 218 & - 55 \\ 83 & 7 & 82 & 106 \\ 20 & 175 & 143 & 74 \end{array} |$ .

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Langkah 2.2.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.2.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + & - \\ - & + & - & + \\ + & - & + & - \\ - & + & - & + \end{array} |$

Langkah 2.2.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.2.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 239 & 218 & - 55 \\ 7 & 82 & 106 \\ 175 & 143 & 74 \end{array} |$

Langkah 2.2.1.4

Multiply element $a_{11}$ by its cofactor.

$169 | \begin{array}{c} 239 & 218 & - 55 \\ 7 & 82 & 106 \\ 175 & 143 & 74 \end{array} |$

Langkah 2.2.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} |$

Langkah 2.2.1.6

Multiply element $a_{12}$ by its cofactor.

$164 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} |$

Langkah 2.2.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} |$

Langkah 2.2.1.8

Multiply element $a_{13}$ by its cofactor.

$18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} |$

Langkah 2.2.1.9

The minor for $a_{14}$ is the determinant with row $1$ and column $4$ deleted.

$| \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |$

Langkah 2.2.1.10

Multiply element $a_{14}$ by its cofactor.

$- 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |$

Langkah 2.2.1.11

Add the terms together.

$44 (169 | \begin{array}{c} 239 & 218 & - 55 \\ 7 & 82 & 106 \\ 175 & 143 & 74 \end{array} | + 164 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} | + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.2

Evaluasi $| \begin{array}{c} 239 & 218 & - 55 \\ 7 & 82 & 106 \\ 175 & 143 & 74 \end{array} |$ .

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Langkah 2.2.2.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.2.2.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 2.2.2.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.2.2.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} |$

Langkah 2.2.2.1.4

Multiply element $a_{11}$ by its cofactor.

$239 | \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} |$

Langkah 2.2.2.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} |$

Langkah 2.2.2.1.6

Multiply element $a_{12}$ by its cofactor.

$- 218 | \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} |$

Langkah 2.2.2.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |$

Langkah 2.2.2.1.8

Multiply element $a_{13}$ by its cofactor.

$- 55 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |$

Langkah 2.2.2.1.9

Add the terms together.

$44 (169 (239 | \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} | - 218 | \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} | - 55 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |) + 164 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} | + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.2.2

Evaluasi $| \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} |$ .

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Langkah 2.2.2.2.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 (169 (239 (82 \cdot 74 - 143 \cdot 106) - 218 | \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} | - 55 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |) + 164 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} | + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.2.2.2

Sederhanakan determinannya.

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Langkah 2.2.2.2.2.1

Sederhanakan setiap suku.

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Langkah 2.2.2.2.2.1.1

Kalikan $82$ dengan $74$ .

$44 (169 (239 (6068 - 143 \cdot 106) - 218 | \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} | - 55 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |) + 164 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} | + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.2.2.2.1.2

Kalikan $- 143$ dengan $106$ .

$44 (169 (239 (6068 - 15158) - 218 | \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} | - 55 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |) + 164 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} | + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.2.2.2.2

Kurangi $15158$ dengan $6068$ .

$44 (169 (239 \cdot - 9090 - 218 | \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} | - 55 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |) + 164 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} | + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.2.3

Evaluasi $| \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} |$ .

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Langkah 2.2.2.3.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 (169 (239 \cdot - 9090 - 218 (7 \cdot 74 - 175 \cdot 106) - 55 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |) + 164 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} | + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.2.3.2

Sederhanakan determinannya.

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Langkah 2.2.2.3.2.1

Sederhanakan setiap suku.

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Langkah 2.2.2.3.2.1.1

Kalikan $7$ dengan $74$ .

$44 (169 (239 \cdot - 9090 - 218 (518 - 175 \cdot 106) - 55 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |) + 164 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} | + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.2.3.2.1.2

Kalikan $- 175$ dengan $106$ .

$44 (169 (239 \cdot - 9090 - 218 (518 - 18550) - 55 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |) + 164 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} | + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.2.3.2.2

Kurangi $18550$ dengan $518$ .

$44 (169 (239 \cdot - 9090 - 218 \cdot - 18032 - 55 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |) + 164 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} | + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.2.4

Evaluasi $| \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |$ .

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Langkah 2.2.2.4.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 (169 (239 \cdot - 9090 - 218 \cdot - 18032 - 55 (7 \cdot 143 - 175 \cdot 82)) + 164 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} | + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.2.4.2

Sederhanakan determinannya.

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Langkah 2.2.2.4.2.1

Sederhanakan setiap suku.

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Langkah 2.2.2.4.2.1.1

Kalikan $7$ dengan $143$ .

$44 (169 (239 \cdot - 9090 - 218 \cdot - 18032 - 55 (1001 - 175 \cdot 82)) + 164 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} | + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.2.4.2.1.2

Kalikan $- 175$ dengan $82$ .

$44 (169 (239 \cdot - 9090 - 218 \cdot - 18032 - 55 (1001 - 14350)) + 164 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} | + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.2.4.2.2

Kurangi $14350$ dengan $1001$ .

$44 (169 (239 \cdot - 9090 - 218 \cdot - 18032 - 55 \cdot - 13349) + 164 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} | + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.2.5

Sederhanakan determinannya.

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Langkah 2.2.2.5.1

Sederhanakan setiap suku.

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Langkah 2.2.2.5.1.1

Kalikan $239$ dengan $- 9090$ .

$44 (169 (- 2172510 - 218 \cdot - 18032 - 55 \cdot - 13349) + 164 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} | + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.2.5.1.2

Kalikan $- 218$ dengan $- 18032$ .

$44 (169 (- 2172510 + 3930976 - 55 \cdot - 13349) + 164 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} | + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.2.5.1.3

Kalikan $- 55$ dengan $- 13349$ .

$44 (169 (- 2172510 + 3930976 + 734195) + 164 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} | + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.2.5.2

Tambahkan $- 2172510$ dan $3930976$ .

$44 (169 (1758466 + 734195) + 164 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} | + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.2.5.3

Tambahkan $1758466$ dan $734195$ .

$44 (169 \cdot 2492661 + 164 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} | + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.3

Evaluasi $| \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} |$ .

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Langkah 2.2.3.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.2.3.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 2.2.3.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.2.3.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} |$

Langkah 2.2.3.1.4

Multiply element $a_{11}$ by its cofactor.

$- 82 | \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} |$

Langkah 2.2.3.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} |$

Langkah 2.2.3.1.6

Multiply element $a_{12}$ by its cofactor.

$- 218 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} |$

Langkah 2.2.3.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |$

Langkah 2.2.3.1.8

Multiply element $a_{13}$ by its cofactor.

$- 55 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |$

Langkah 2.2.3.1.9

Add the terms together.

$44 (169 \cdot 2492661 + 164 (- 82 | \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} | - 218 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | - 55 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |) + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.3.2

Evaluasi $| \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} |$ .

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Langkah 2.2.3.2.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 (169 \cdot 2492661 + 164 (- 82 (82 \cdot 74 - 143 \cdot 106) - 218 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | - 55 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |) + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.3.2.2

Sederhanakan determinannya.

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Langkah 2.2.3.2.2.1

Sederhanakan setiap suku.

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Langkah 2.2.3.2.2.1.1

Kalikan $82$ dengan $74$ .

$44 (169 \cdot 2492661 + 164 (- 82 (6068 - 143 \cdot 106) - 218 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | - 55 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |) + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.3.2.2.1.2

Kalikan $- 143$ dengan $106$ .

$44 (169 \cdot 2492661 + 164 (- 82 (6068 - 15158) - 218 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | - 55 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |) + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.3.2.2.2

Kurangi $15158$ dengan $6068$ .

$44 (169 \cdot 2492661 + 164 (- 82 \cdot - 9090 - 218 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | - 55 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |) + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.3.3

Evaluasi $| \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} |$ .

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Langkah 2.2.3.3.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 (169 \cdot 2492661 + 164 (- 82 \cdot - 9090 - 218 (83 \cdot 74 - 20 \cdot 106) - 55 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |) + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.3.3.2

Sederhanakan determinannya.

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Langkah 2.2.3.3.2.1

Sederhanakan setiap suku.

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Langkah 2.2.3.3.2.1.1

Kalikan $83$ dengan $74$ .

$44 (169 \cdot 2492661 + 164 (- 82 \cdot - 9090 - 218 (6142 - 20 \cdot 106) - 55 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |) + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.3.3.2.1.2

Kalikan $- 20$ dengan $106$ .

$44 (169 \cdot 2492661 + 164 (- 82 \cdot - 9090 - 218 (6142 - 2120) - 55 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |) + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.3.3.2.2

Kurangi $2120$ dengan $6142$ .

$44 (169 \cdot 2492661 + 164 (- 82 \cdot - 9090 - 218 \cdot 4022 - 55 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |) + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.3.4

Evaluasi $| \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |$ .

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Langkah 2.2.3.4.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 (169 \cdot 2492661 + 164 (- 82 \cdot - 9090 - 218 \cdot 4022 - 55 (83 \cdot 143 - 20 \cdot 82)) + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.3.4.2

Sederhanakan determinannya.

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Langkah 2.2.3.4.2.1

Sederhanakan setiap suku.

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Langkah 2.2.3.4.2.1.1

Kalikan $83$ dengan $143$ .

$44 (169 \cdot 2492661 + 164 (- 82 \cdot - 9090 - 218 \cdot 4022 - 55 (11869 - 20 \cdot 82)) + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.3.4.2.1.2

Kalikan $- 20$ dengan $82$ .

$44 (169 \cdot 2492661 + 164 (- 82 \cdot - 9090 - 218 \cdot 4022 - 55 (11869 - 1640)) + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.3.4.2.2

Kurangi $1640$ dengan $11869$ .

$44 (169 \cdot 2492661 + 164 (- 82 \cdot - 9090 - 218 \cdot 4022 - 55 \cdot 10229) + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.3.5

Sederhanakan determinannya.

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Langkah 2.2.3.5.1

Sederhanakan setiap suku.

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Langkah 2.2.3.5.1.1

Kalikan $- 82$ dengan $- 9090$ .

$44 (169 \cdot 2492661 + 164 (745380 - 218 \cdot 4022 - 55 \cdot 10229) + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.3.5.1.2

Kalikan $- 218$ dengan $4022$ .

$44 (169 \cdot 2492661 + 164 (745380 - 876796 - 55 \cdot 10229) + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.3.5.1.3

Kalikan $- 55$ dengan $10229$ .

$44 (169 \cdot 2492661 + 164 (745380 - 876796 - 562595) + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.3.5.2

Kurangi $876796$ dengan $745380$ .

$44 (169 \cdot 2492661 + 164 (- 131416 - 562595) + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.3.5.3

Kurangi $562595$ dengan $- 131416$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.4

Evaluasi $| \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} |$ .

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Langkah 2.2.4.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.2.4.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 2.2.4.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.2.4.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} |$

Langkah 2.2.4.1.4

Multiply element $a_{11}$ by its cofactor.

$- 82 | \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} |$

Langkah 2.2.4.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} |$

Langkah 2.2.4.1.6

Multiply element $a_{12}$ by its cofactor.

$- 239 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} |$

Langkah 2.2.4.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$

Langkah 2.2.4.1.8

Multiply element $a_{13}$ by its cofactor.

$- 55 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$

Langkah 2.2.4.1.9

Add the terms together.

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 (- 82 | \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} | - 239 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | - 55 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.4.2

Evaluasi $| \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} |$ .

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Langkah 2.2.4.2.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 (- 82 (7 \cdot 74 - 175 \cdot 106) - 239 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | - 55 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.4.2.2

Sederhanakan determinannya.

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Langkah 2.2.4.2.2.1

Sederhanakan setiap suku.

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Langkah 2.2.4.2.2.1.1

Kalikan $7$ dengan $74$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 (- 82 (518 - 175 \cdot 106) - 239 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | - 55 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.4.2.2.1.2

Kalikan $- 175$ dengan $106$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 (- 82 (518 - 18550) - 239 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | - 55 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.4.2.2.2

Kurangi $18550$ dengan $518$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 (- 82 \cdot - 18032 - 239 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | - 55 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.4.3

Evaluasi $| \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} |$ .

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Langkah 2.2.4.3.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 (- 82 \cdot - 18032 - 239 (83 \cdot 74 - 20 \cdot 106) - 55 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.4.3.2

Sederhanakan determinannya.

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Langkah 2.2.4.3.2.1

Sederhanakan setiap suku.

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Langkah 2.2.4.3.2.1.1

Kalikan $83$ dengan $74$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 (- 82 \cdot - 18032 - 239 (6142 - 20 \cdot 106) - 55 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.4.3.2.1.2

Kalikan $- 20$ dengan $106$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 (- 82 \cdot - 18032 - 239 (6142 - 2120) - 55 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.4.3.2.2

Kurangi $2120$ dengan $6142$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 (- 82 \cdot - 18032 - 239 \cdot 4022 - 55 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.4.4

Evaluasi $| \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$ .

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Langkah 2.2.4.4.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 (- 82 \cdot - 18032 - 239 \cdot 4022 - 55 (83 \cdot 175 - 20 \cdot 7)) - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.4.4.2

Sederhanakan determinannya.

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Langkah 2.2.4.4.2.1

Sederhanakan setiap suku.

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Langkah 2.2.4.4.2.1.1

Kalikan $83$ dengan $175$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 (- 82 \cdot - 18032 - 239 \cdot 4022 - 55 (14525 - 20 \cdot 7)) - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.4.4.2.1.2

Kalikan $- 20$ dengan $7$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 (- 82 \cdot - 18032 - 239 \cdot 4022 - 55 (14525 - 140)) - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.4.4.2.2

Kurangi $140$ dengan $14525$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 (- 82 \cdot - 18032 - 239 \cdot 4022 - 55 \cdot 14385) - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.4.5

Sederhanakan determinannya.

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Langkah 2.2.4.5.1

Sederhanakan setiap suku.

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Langkah 2.2.4.5.1.1

Kalikan $- 82$ dengan $- 18032$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 (1478624 - 239 \cdot 4022 - 55 \cdot 14385) - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.4.5.1.2

Kalikan $- 239$ dengan $4022$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 (1478624 - 961258 - 55 \cdot 14385) - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.4.5.1.3

Kalikan $- 55$ dengan $14385$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 (1478624 - 961258 - 791175) - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.4.5.2

Kurangi $961258$ dengan $1478624$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 (517366 - 791175) - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.4.5.3

Kurangi $791175$ dengan $517366$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 \cdot - 273809 - 105 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.5

Evaluasi $| \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |$ .

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Langkah 2.2.5.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.2.5.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 2.2.5.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.2.5.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |$

Langkah 2.2.5.1.4

Multiply element $a_{11}$ by its cofactor.

$- 82 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |$

Langkah 2.2.5.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |$

Langkah 2.2.5.1.6

Multiply element $a_{12}$ by its cofactor.

$- 239 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |$

Langkah 2.2.5.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$

Langkah 2.2.5.1.8

Multiply element $a_{13}$ by its cofactor.

$218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$

Langkah 2.2.5.1.9

Add the terms together.

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 \cdot - 273809 - 105 (- 82 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} | - 239 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} | + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |)) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.5.2

Evaluasi $| \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |$ .

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Langkah 2.2.5.2.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 \cdot - 273809 - 105 (- 82 (7 \cdot 143 - 175 \cdot 82) - 239 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} | + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |)) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.5.2.2

Sederhanakan determinannya.

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Langkah 2.2.5.2.2.1

Sederhanakan setiap suku.

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Langkah 2.2.5.2.2.1.1

Kalikan $7$ dengan $143$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 \cdot - 273809 - 105 (- 82 (1001 - 175 \cdot 82) - 239 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} | + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |)) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.5.2.2.1.2

Kalikan $- 175$ dengan $82$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 \cdot - 273809 - 105 (- 82 (1001 - 14350) - 239 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} | + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |)) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.5.2.2.2

Kurangi $14350$ dengan $1001$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 \cdot - 273809 - 105 (- 82 \cdot - 13349 - 239 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} | + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |)) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.5.3

Evaluasi $| \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |$ .

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Langkah 2.2.5.3.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 \cdot - 273809 - 105 (- 82 \cdot - 13349 - 239 (83 \cdot 143 - 20 \cdot 82) + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |)) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.5.3.2

Sederhanakan determinannya.

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Langkah 2.2.5.3.2.1

Sederhanakan setiap suku.

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Langkah 2.2.5.3.2.1.1

Kalikan $83$ dengan $143$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 \cdot - 273809 - 105 (- 82 \cdot - 13349 - 239 (11869 - 20 \cdot 82) + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |)) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.5.3.2.1.2

Kalikan $- 20$ dengan $82$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 \cdot - 273809 - 105 (- 82 \cdot - 13349 - 239 (11869 - 1640) + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |)) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.5.3.2.2

Kurangi $1640$ dengan $11869$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 \cdot - 273809 - 105 (- 82 \cdot - 13349 - 239 \cdot 10229 + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |)) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.5.4

Evaluasi $| \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$ .

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Langkah 2.2.5.4.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 \cdot - 273809 - 105 (- 82 \cdot - 13349 - 239 \cdot 10229 + 218 (83 \cdot 175 - 20 \cdot 7))) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.5.4.2

Sederhanakan determinannya.

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Langkah 2.2.5.4.2.1

Sederhanakan setiap suku.

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Langkah 2.2.5.4.2.1.1

Kalikan $83$ dengan $175$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 \cdot - 273809 - 105 (- 82 \cdot - 13349 - 239 \cdot 10229 + 218 (14525 - 20 \cdot 7))) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.5.4.2.1.2

Kalikan $- 20$ dengan $7$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 \cdot - 273809 - 105 (- 82 \cdot - 13349 - 239 \cdot 10229 + 218 (14525 - 140))) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.5.4.2.2

Kurangi $140$ dengan $14525$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 \cdot - 273809 - 105 (- 82 \cdot - 13349 - 239 \cdot 10229 + 218 \cdot 14385)) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.5.5

Sederhanakan determinannya.

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Langkah 2.2.5.5.1

Sederhanakan setiap suku.

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Langkah 2.2.5.5.1.1

Kalikan $- 82$ dengan $- 13349$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 \cdot - 273809 - 105 (1094618 - 239 \cdot 10229 + 218 \cdot 14385)) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.5.5.1.2

Kalikan $- 239$ dengan $10229$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 \cdot - 273809 - 105 (1094618 - 2444731 + 218 \cdot 14385)) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.5.5.1.3

Kalikan $218$ dengan $14385$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 \cdot - 273809 - 105 (1094618 - 2444731 + 3135930)) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.5.5.2

Kurangi $2444731$ dengan $1094618$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 \cdot - 273809 - 105 (- 1350113 + 3135930)) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.5.5.3

Tambahkan $- 1350113$ dan $3135930$ .

$44 (169 \cdot 2492661 + 164 \cdot - 694011 + 18 \cdot - 273809 - 105 \cdot 1785817) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.6

Sederhanakan determinannya.

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Langkah 2.2.6.1

Sederhanakan setiap suku.

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Langkah 2.2.6.1.1

Kalikan $169$ dengan $2492661$ .

$44 (421259709 + 164 \cdot - 694011 + 18 \cdot - 273809 - 105 \cdot 1785817) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.6.1.2

Kalikan $164$ dengan $- 694011$ .

$44 (421259709 - 113817804 + 18 \cdot - 273809 - 105 \cdot 1785817) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.6.1.3

Kalikan $18$ dengan $- 273809$ .

$44 (421259709 - 113817804 - 4928562 - 105 \cdot 1785817) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.6.1.4

Kalikan $- 105$ dengan $1785817$ .

$44 (421259709 - 113817804 - 4928562 - 187510785) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.6.2

Kurangi $113817804$ dengan $421259709$ .

$44 (307441905 - 4928562 - 187510785) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.6.3

Kurangi $4928562$ dengan $307441905$ .

$44 (302513343 - 187510785) - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.2.6.4

Kurangi $187510785$ dengan $302513343$ .

$44 \cdot 115002558 - 75 | \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} | - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3

Evaluasi $| \begin{array}{c} 20 & - 164 & 18 & 105 \\ 113 & 239 & 218 & - 55 \\ 119 & 7 & 82 & 106 \\ 162 & 175 & 143 & 74 \end{array} |$ .

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Langkah 2.3.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.3.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + & - \\ - & + & - & + \\ + & - & + & - \\ - & + & - & + \end{array} |$

Langkah 2.3.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.3.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 239 & 218 & - 55 \\ 7 & 82 & 106 \\ 175 & 143 & 74 \end{array} |$

Langkah 2.3.1.4

Multiply element $a_{11}$ by its cofactor.

$20 | \begin{array}{c} 239 & 218 & - 55 \\ 7 & 82 & 106 \\ 175 & 143 & 74 \end{array} |$

Langkah 2.3.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} |$

Langkah 2.3.1.6

Multiply element $a_{12}$ by its cofactor.

$164 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} |$

Langkah 2.3.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} |$

Langkah 2.3.1.8

Multiply element $a_{13}$ by its cofactor.

$18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} |$

Langkah 2.3.1.9

The minor for $a_{14}$ is the determinant with row $1$ and column $4$ deleted.

$| \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |$

Langkah 2.3.1.10

Multiply element $a_{14}$ by its cofactor.

$- 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |$

Langkah 2.3.1.11

Add the terms together.

$44 \cdot 115002558 - 75 (20 | \begin{array}{c} 239 & 218 & - 55 \\ 7 & 82 & 106 \\ 175 & 143 & 74 \end{array} | + 164 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.2

Evaluasi $| \begin{array}{c} 239 & 218 & - 55 \\ 7 & 82 & 106 \\ 175 & 143 & 74 \end{array} |$ .

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Langkah 2.3.2.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.3.2.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 2.3.2.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.3.2.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} |$

Langkah 2.3.2.1.4

Multiply element $a_{11}$ by its cofactor.

$239 | \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} |$

Langkah 2.3.2.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} |$

Langkah 2.3.2.1.6

Multiply element $a_{12}$ by its cofactor.

$- 218 | \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} |$

Langkah 2.3.2.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |$

Langkah 2.3.2.1.8

Multiply element $a_{13}$ by its cofactor.

$- 55 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |$

Langkah 2.3.2.1.9

Add the terms together.

$44 \cdot 115002558 - 75 (20 (239 | \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} | - 218 | \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} | - 55 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |) + 164 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.2.2

Evaluasi $| \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} |$ .

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Langkah 2.3.2.2.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 (20 (239 (82 \cdot 74 - 143 \cdot 106) - 218 | \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} | - 55 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |) + 164 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.2.2.2

Sederhanakan determinannya.

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Langkah 2.3.2.2.2.1

Sederhanakan setiap suku.

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Langkah 2.3.2.2.2.1.1

Kalikan $82$ dengan $74$ .

$44 \cdot 115002558 - 75 (20 (239 (6068 - 143 \cdot 106) - 218 | \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} | - 55 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |) + 164 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.2.2.2.1.2

Kalikan $- 143$ dengan $106$ .

$44 \cdot 115002558 - 75 (20 (239 (6068 - 15158) - 218 | \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} | - 55 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |) + 164 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.2.2.2.2

Kurangi $15158$ dengan $6068$ .

$44 \cdot 115002558 - 75 (20 (239 \cdot - 9090 - 218 | \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} | - 55 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |) + 164 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.2.3

Evaluasi $| \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} |$ .

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Langkah 2.3.2.3.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 (20 (239 \cdot - 9090 - 218 (7 \cdot 74 - 175 \cdot 106) - 55 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |) + 164 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.2.3.2

Sederhanakan determinannya.

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Langkah 2.3.2.3.2.1

Sederhanakan setiap suku.

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Langkah 2.3.2.3.2.1.1

Kalikan $7$ dengan $74$ .

$44 \cdot 115002558 - 75 (20 (239 \cdot - 9090 - 218 (518 - 175 \cdot 106) - 55 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |) + 164 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.2.3.2.1.2

Kalikan $- 175$ dengan $106$ .

$44 \cdot 115002558 - 75 (20 (239 \cdot - 9090 - 218 (518 - 18550) - 55 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |) + 164 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.2.3.2.2

Kurangi $18550$ dengan $518$ .

$44 \cdot 115002558 - 75 (20 (239 \cdot - 9090 - 218 \cdot - 18032 - 55 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |) + 164 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.2.4

Evaluasi $| \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |$ .

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Langkah 2.3.2.4.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 (20 (239 \cdot - 9090 - 218 \cdot - 18032 - 55 (7 \cdot 143 - 175 \cdot 82)) + 164 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.2.4.2

Sederhanakan determinannya.

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Langkah 2.3.2.4.2.1

Sederhanakan setiap suku.

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Langkah 2.3.2.4.2.1.1

Kalikan $7$ dengan $143$ .

$44 \cdot 115002558 - 75 (20 (239 \cdot - 9090 - 218 \cdot - 18032 - 55 (1001 - 175 \cdot 82)) + 164 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.2.4.2.1.2

Kalikan $- 175$ dengan $82$ .

$44 \cdot 115002558 - 75 (20 (239 \cdot - 9090 - 218 \cdot - 18032 - 55 (1001 - 14350)) + 164 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.2.4.2.2

Kurangi $14350$ dengan $1001$ .

$44 \cdot 115002558 - 75 (20 (239 \cdot - 9090 - 218 \cdot - 18032 - 55 \cdot - 13349) + 164 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.2.5

Sederhanakan determinannya.

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Langkah 2.3.2.5.1

Sederhanakan setiap suku.

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Langkah 2.3.2.5.1.1

Kalikan $239$ dengan $- 9090$ .

$44 \cdot 115002558 - 75 (20 (- 2172510 - 218 \cdot - 18032 - 55 \cdot - 13349) + 164 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.2.5.1.2

Kalikan $- 218$ dengan $- 18032$ .

$44 \cdot 115002558 - 75 (20 (- 2172510 + 3930976 - 55 \cdot - 13349) + 164 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.2.5.1.3

Kalikan $- 55$ dengan $- 13349$ .

$44 \cdot 115002558 - 75 (20 (- 2172510 + 3930976 + 734195) + 164 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.2.5.2

Tambahkan $- 2172510$ dan $3930976$ .

$44 \cdot 115002558 - 75 (20 (1758466 + 734195) + 164 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.2.5.3

Tambahkan $1758466$ dan $734195$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.3

Evaluasi $| \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} |$ .

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Langkah 2.3.3.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.3.3.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 2.3.3.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.3.3.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} |$

Langkah 2.3.3.1.4

Multiply element $a_{11}$ by its cofactor.

$113 | \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} |$

Langkah 2.3.3.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} |$

Langkah 2.3.3.1.6

Multiply element $a_{12}$ by its cofactor.

$- 218 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} |$

Langkah 2.3.3.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$

Langkah 2.3.3.1.8

Multiply element $a_{13}$ by its cofactor.

$- 55 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$

Langkah 2.3.3.1.9

Add the terms together.

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 (113 | \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} | - 218 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |) + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.3.2

Evaluasi $| \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} |$ .

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Langkah 2.3.3.2.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 (113 (82 \cdot 74 - 143 \cdot 106) - 218 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |) + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.3.2.2

Sederhanakan determinannya.

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Langkah 2.3.3.2.2.1

Sederhanakan setiap suku.

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Langkah 2.3.3.2.2.1.1

Kalikan $82$ dengan $74$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 (113 (6068 - 143 \cdot 106) - 218 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |) + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.3.2.2.1.2

Kalikan $- 143$ dengan $106$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 (113 (6068 - 15158) - 218 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |) + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.3.2.2.2

Kurangi $15158$ dengan $6068$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 (113 \cdot - 9090 - 218 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |) + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.3.3

Evaluasi $| \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} |$ .

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Langkah 2.3.3.3.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 (113 \cdot - 9090 - 218 (119 \cdot 74 - 162 \cdot 106) - 55 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |) + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.3.3.2

Sederhanakan determinannya.

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Langkah 2.3.3.3.2.1

Sederhanakan setiap suku.

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Langkah 2.3.3.3.2.1.1

Kalikan $119$ dengan $74$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 (113 \cdot - 9090 - 218 (8806 - 162 \cdot 106) - 55 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |) + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.3.3.2.1.2

Kalikan $- 162$ dengan $106$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 (113 \cdot - 9090 - 218 (8806 - 17172) - 55 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |) + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.3.3.2.2

Kurangi $17172$ dengan $8806$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 (113 \cdot - 9090 - 218 \cdot - 8366 - 55 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |) + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.3.4

Evaluasi $| \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$ .

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Langkah 2.3.3.4.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 (113 \cdot - 9090 - 218 \cdot - 8366 - 55 (119 \cdot 143 - 162 \cdot 82)) + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.3.4.2

Sederhanakan determinannya.

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Langkah 2.3.3.4.2.1

Sederhanakan setiap suku.

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Langkah 2.3.3.4.2.1.1

Kalikan $119$ dengan $143$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 (113 \cdot - 9090 - 218 \cdot - 8366 - 55 (17017 - 162 \cdot 82)) + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.3.4.2.1.2

Kalikan $- 162$ dengan $82$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 (113 \cdot - 9090 - 218 \cdot - 8366 - 55 (17017 - 13284)) + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.3.4.2.2

Kurangi $13284$ dengan $17017$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 (113 \cdot - 9090 - 218 \cdot - 8366 - 55 \cdot 3733) + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.3.5

Sederhanakan determinannya.

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Langkah 2.3.3.5.1

Sederhanakan setiap suku.

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Langkah 2.3.3.5.1.1

Kalikan $113$ dengan $- 9090$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 (- 1027170 - 218 \cdot - 8366 - 55 \cdot 3733) + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.3.5.1.2

Kalikan $- 218$ dengan $- 8366$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 (- 1027170 + 1823788 - 55 \cdot 3733) + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.3.5.1.3

Kalikan $- 55$ dengan $3733$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 (- 1027170 + 1823788 - 205315) + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.3.5.2

Tambahkan $- 1027170$ dan $1823788$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 (796618 - 205315) + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.3.5.3

Kurangi $205315$ dengan $796618$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.4

Evaluasi $| \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} |$ .

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Langkah 2.3.4.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.3.4.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 2.3.4.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.3.4.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} |$

Langkah 2.3.4.1.4

Multiply element $a_{11}$ by its cofactor.

$113 | \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} |$

Langkah 2.3.4.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} |$

Langkah 2.3.4.1.6

Multiply element $a_{12}$ by its cofactor.

$- 239 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} |$

Langkah 2.3.4.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$

Langkah 2.3.4.1.8

Multiply element $a_{13}$ by its cofactor.

$- 55 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$

Langkah 2.3.4.1.9

Add the terms together.

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 (113 | \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} | - 239 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.4.2

Evaluasi $| \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} |$ .

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Langkah 2.3.4.2.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 (113 (7 \cdot 74 - 175 \cdot 106) - 239 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.4.2.2

Sederhanakan determinannya.

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Langkah 2.3.4.2.2.1

Sederhanakan setiap suku.

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Langkah 2.3.4.2.2.1.1

Kalikan $7$ dengan $74$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 (113 (518 - 175 \cdot 106) - 239 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.4.2.2.1.2

Kalikan $- 175$ dengan $106$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 (113 (518 - 18550) - 239 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.4.2.2.2

Kurangi $18550$ dengan $518$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 (113 \cdot - 18032 - 239 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.4.3

Evaluasi $| \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} |$ .

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Langkah 2.3.4.3.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 (113 \cdot - 18032 - 239 (119 \cdot 74 - 162 \cdot 106) - 55 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.4.3.2

Sederhanakan determinannya.

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Langkah 2.3.4.3.2.1

Sederhanakan setiap suku.

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Langkah 2.3.4.3.2.1.1

Kalikan $119$ dengan $74$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 (113 \cdot - 18032 - 239 (8806 - 162 \cdot 106) - 55 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.4.3.2.1.2

Kalikan $- 162$ dengan $106$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 (113 \cdot - 18032 - 239 (8806 - 17172) - 55 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.4.3.2.2

Kurangi $17172$ dengan $8806$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 (113 \cdot - 18032 - 239 \cdot - 8366 - 55 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.4.4

Evaluasi $| \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$ .

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Langkah 2.3.4.4.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 (113 \cdot - 18032 - 239 \cdot - 8366 - 55 (119 \cdot 175 - 162 \cdot 7)) - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.4.4.2

Sederhanakan determinannya.

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Langkah 2.3.4.4.2.1

Sederhanakan setiap suku.

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Langkah 2.3.4.4.2.1.1

Kalikan $119$ dengan $175$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 (113 \cdot - 18032 - 239 \cdot - 8366 - 55 (20825 - 162 \cdot 7)) - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.4.4.2.1.2

Kalikan $- 162$ dengan $7$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 (113 \cdot - 18032 - 239 \cdot - 8366 - 55 (20825 - 1134)) - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.4.4.2.2

Kurangi $1134$ dengan $20825$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 (113 \cdot - 18032 - 239 \cdot - 8366 - 55 \cdot 19691) - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.4.5

Sederhanakan determinannya.

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Langkah 2.3.4.5.1

Sederhanakan setiap suku.

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Langkah 2.3.4.5.1.1

Kalikan $113$ dengan $- 18032$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 (- 2037616 - 239 \cdot - 8366 - 55 \cdot 19691) - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.4.5.1.2

Kalikan $- 239$ dengan $- 8366$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 (- 2037616 + 1999474 - 55 \cdot 19691) - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.4.5.1.3

Kalikan $- 55$ dengan $19691$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 (- 2037616 + 1999474 - 1083005) - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.4.5.2

Tambahkan $- 2037616$ dan $1999474$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 (- 38142 - 1083005) - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.4.5.3

Kurangi $1083005$ dengan $- 38142$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 \cdot - 1121147 - 105 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.5

Evaluasi $| \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |$ .

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Langkah 2.3.5.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.3.5.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 2.3.5.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.3.5.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |$

Langkah 2.3.5.1.4

Multiply element $a_{11}$ by its cofactor.

$113 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |$

Langkah 2.3.5.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$

Langkah 2.3.5.1.6

Multiply element $a_{12}$ by its cofactor.

$- 239 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$

Langkah 2.3.5.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$

Langkah 2.3.5.1.8

Multiply element $a_{13}$ by its cofactor.

$218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$

Langkah 2.3.5.1.9

Add the terms together.

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 \cdot - 1121147 - 105 (113 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} | - 239 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |)) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.5.2

Evaluasi $| \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |$ .

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Langkah 2.3.5.2.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 \cdot - 1121147 - 105 (113 (7 \cdot 143 - 175 \cdot 82) - 239 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |)) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.5.2.2

Sederhanakan determinannya.

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Langkah 2.3.5.2.2.1

Sederhanakan setiap suku.

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Langkah 2.3.5.2.2.1.1

Kalikan $7$ dengan $143$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 \cdot - 1121147 - 105 (113 (1001 - 175 \cdot 82) - 239 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |)) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.5.2.2.1.2

Kalikan $- 175$ dengan $82$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 \cdot - 1121147 - 105 (113 (1001 - 14350) - 239 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |)) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.5.2.2.2

Kurangi $14350$ dengan $1001$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 \cdot - 1121147 - 105 (113 \cdot - 13349 - 239 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |)) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.5.3

Evaluasi $| \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$ .

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Langkah 2.3.5.3.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 \cdot - 1121147 - 105 (113 \cdot - 13349 - 239 (119 \cdot 143 - 162 \cdot 82) + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |)) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.5.3.2

Sederhanakan determinannya.

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Langkah 2.3.5.3.2.1

Sederhanakan setiap suku.

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Langkah 2.3.5.3.2.1.1

Kalikan $119$ dengan $143$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 \cdot - 1121147 - 105 (113 \cdot - 13349 - 239 (17017 - 162 \cdot 82) + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |)) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.5.3.2.1.2

Kalikan $- 162$ dengan $82$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 \cdot - 1121147 - 105 (113 \cdot - 13349 - 239 (17017 - 13284) + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |)) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.5.3.2.2

Kurangi $13284$ dengan $17017$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 \cdot - 1121147 - 105 (113 \cdot - 13349 - 239 \cdot 3733 + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |)) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.5.4

Evaluasi $| \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$ .

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Langkah 2.3.5.4.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 \cdot - 1121147 - 105 (113 \cdot - 13349 - 239 \cdot 3733 + 218 (119 \cdot 175 - 162 \cdot 7))) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.5.4.2

Sederhanakan determinannya.

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Langkah 2.3.5.4.2.1

Sederhanakan setiap suku.

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Langkah 2.3.5.4.2.1.1

Kalikan $119$ dengan $175$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 \cdot - 1121147 - 105 (113 \cdot - 13349 - 239 \cdot 3733 + 218 (20825 - 162 \cdot 7))) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.5.4.2.1.2

Kalikan $- 162$ dengan $7$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 \cdot - 1121147 - 105 (113 \cdot - 13349 - 239 \cdot 3733 + 218 (20825 - 1134))) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.5.4.2.2

Kurangi $1134$ dengan $20825$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 \cdot - 1121147 - 105 (113 \cdot - 13349 - 239 \cdot 3733 + 218 \cdot 19691)) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.5.5

Sederhanakan determinannya.

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Langkah 2.3.5.5.1

Sederhanakan setiap suku.

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Langkah 2.3.5.5.1.1

Kalikan $113$ dengan $- 13349$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 \cdot - 1121147 - 105 (- 1508437 - 239 \cdot 3733 + 218 \cdot 19691)) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.5.5.1.2

Kalikan $- 239$ dengan $3733$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 \cdot - 1121147 - 105 (- 1508437 - 892187 + 218 \cdot 19691)) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.5.5.1.3

Kalikan $218$ dengan $19691$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 \cdot - 1121147 - 105 (- 1508437 - 892187 + 4292638)) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.5.5.2

Kurangi $892187$ dengan $- 1508437$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 \cdot - 1121147 - 105 (- 2400624 + 4292638)) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.5.5.3

Tambahkan $- 2400624$ dan $4292638$ .

$44 \cdot 115002558 - 75 (20 \cdot 2492661 + 164 \cdot 591303 + 18 \cdot - 1121147 - 105 \cdot 1892014) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.6

Sederhanakan determinannya.

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Langkah 2.3.6.1

Sederhanakan setiap suku.

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Langkah 2.3.6.1.1

Kalikan $20$ dengan $2492661$ .

$44 \cdot 115002558 - 75 (49853220 + 164 \cdot 591303 + 18 \cdot - 1121147 - 105 \cdot 1892014) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.6.1.2

Kalikan $164$ dengan $591303$ .

$44 \cdot 115002558 - 75 (49853220 + 96973692 + 18 \cdot - 1121147 - 105 \cdot 1892014) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.6.1.3

Kalikan $18$ dengan $- 1121147$ .

$44 \cdot 115002558 - 75 (49853220 + 96973692 - 20180646 - 105 \cdot 1892014) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.6.1.4

Kalikan $- 105$ dengan $1892014$ .

$44 \cdot 115002558 - 75 (49853220 + 96973692 - 20180646 - 198661470) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.6.2

Tambahkan $49853220$ dan $96973692$ .

$44 \cdot 115002558 - 75 (146826912 - 20180646 - 198661470) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.6.3

Kurangi $20180646$ dengan $146826912$ .

$44 \cdot 115002558 - 75 (126646266 - 198661470) - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.3.6.4

Kurangi $198661470$ dengan $126646266$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 | \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} | + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4

Evaluasi $| \begin{array}{c} 20 & 169 & 18 & 105 \\ 113 & - 82 & 218 & - 55 \\ 119 & 83 & 82 & 106 \\ 162 & 20 & 143 & 74 \end{array} |$ .

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Langkah 2.4.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.4.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + & - \\ - & + & - & + \\ + & - & + & - \\ - & + & - & + \end{array} |$

Langkah 2.4.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.4.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} |$

Langkah 2.4.1.4

Multiply element $a_{11}$ by its cofactor.

$20 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} |$

Langkah 2.4.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} |$

Langkah 2.4.1.6

Multiply element $a_{12}$ by its cofactor.

$- 169 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} |$

Langkah 2.4.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} |$

Langkah 2.4.1.8

Multiply element $a_{13}$ by its cofactor.

$18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} |$

Langkah 2.4.1.9

The minor for $a_{14}$ is the determinant with row $1$ and column $4$ deleted.

$| \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |$

Langkah 2.4.1.10

Multiply element $a_{14}$ by its cofactor.

$- 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |$

Langkah 2.4.1.11

Add the terms together.

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 | \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} | - 169 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.2

Evaluasi $| \begin{array}{c} - 82 & 218 & - 55 \\ 83 & 82 & 106 \\ 20 & 143 & 74 \end{array} |$ .

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Langkah 2.4.2.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.4.2.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 2.4.2.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.4.2.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} |$

Langkah 2.4.2.1.4

Multiply element $a_{11}$ by its cofactor.

$- 82 | \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} |$

Langkah 2.4.2.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} |$

Langkah 2.4.2.1.6

Multiply element $a_{12}$ by its cofactor.

$- 218 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} |$

Langkah 2.4.2.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |$

Langkah 2.4.2.1.8

Multiply element $a_{13}$ by its cofactor.

$- 55 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |$

Langkah 2.4.2.1.9

Add the terms together.

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 (- 82 | \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} | - 218 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | - 55 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |) - 169 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.2.2

Evaluasi $| \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} |$ .

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Langkah 2.4.2.2.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 (- 82 (82 \cdot 74 - 143 \cdot 106) - 218 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | - 55 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |) - 169 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.2.2.2

Sederhanakan determinannya.

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Langkah 2.4.2.2.2.1

Sederhanakan setiap suku.

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Langkah 2.4.2.2.2.1.1

Kalikan $82$ dengan $74$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 (- 82 (6068 - 143 \cdot 106) - 218 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | - 55 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |) - 169 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.2.2.2.1.2

Kalikan $- 143$ dengan $106$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 (- 82 (6068 - 15158) - 218 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | - 55 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |) - 169 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.2.2.2.2

Kurangi $15158$ dengan $6068$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 (- 82 \cdot - 9090 - 218 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | - 55 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |) - 169 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.2.3

Evaluasi $| \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} |$ .

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Langkah 2.4.2.3.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 (- 82 \cdot - 9090 - 218 (83 \cdot 74 - 20 \cdot 106) - 55 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |) - 169 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.2.3.2

Sederhanakan determinannya.

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Langkah 2.4.2.3.2.1

Sederhanakan setiap suku.

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Langkah 2.4.2.3.2.1.1

Kalikan $83$ dengan $74$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 (- 82 \cdot - 9090 - 218 (6142 - 20 \cdot 106) - 55 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |) - 169 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.2.3.2.1.2

Kalikan $- 20$ dengan $106$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 (- 82 \cdot - 9090 - 218 (6142 - 2120) - 55 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |) - 169 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.2.3.2.2

Kurangi $2120$ dengan $6142$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 (- 82 \cdot - 9090 - 218 \cdot 4022 - 55 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |) - 169 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.2.4

Evaluasi $| \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |$ .

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Langkah 2.4.2.4.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 (- 82 \cdot - 9090 - 218 \cdot 4022 - 55 (83 \cdot 143 - 20 \cdot 82)) - 169 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.2.4.2

Sederhanakan determinannya.

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Langkah 2.4.2.4.2.1

Sederhanakan setiap suku.

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Langkah 2.4.2.4.2.1.1

Kalikan $83$ dengan $143$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 (- 82 \cdot - 9090 - 218 \cdot 4022 - 55 (11869 - 20 \cdot 82)) - 169 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.2.4.2.1.2

Kalikan $- 20$ dengan $82$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 (- 82 \cdot - 9090 - 218 \cdot 4022 - 55 (11869 - 1640)) - 169 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.2.4.2.2

Kurangi $1640$ dengan $11869$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 (- 82 \cdot - 9090 - 218 \cdot 4022 - 55 \cdot 10229) - 169 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.2.5

Sederhanakan determinannya.

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Langkah 2.4.2.5.1

Sederhanakan setiap suku.

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Langkah 2.4.2.5.1.1

Kalikan $- 82$ dengan $- 9090$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 (745380 - 218 \cdot 4022 - 55 \cdot 10229) - 169 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.2.5.1.2

Kalikan $- 218$ dengan $4022$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 (745380 - 876796 - 55 \cdot 10229) - 169 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.2.5.1.3

Kalikan $- 55$ dengan $10229$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 (745380 - 876796 - 562595) - 169 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.2.5.2

Kurangi $876796$ dengan $745380$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 (- 131416 - 562595) - 169 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.2.5.3

Kurangi $562595$ dengan $- 131416$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 | \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} | + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.3

Evaluasi $| \begin{array}{c} 113 & 218 & - 55 \\ 119 & 82 & 106 \\ 162 & 143 & 74 \end{array} |$ .

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Langkah 2.4.3.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.4.3.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 2.4.3.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.4.3.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} |$

Langkah 2.4.3.1.4

Multiply element $a_{11}$ by its cofactor.

$113 | \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} |$

Langkah 2.4.3.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} |$

Langkah 2.4.3.1.6

Multiply element $a_{12}$ by its cofactor.

$- 218 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} |$

Langkah 2.4.3.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$

Langkah 2.4.3.1.8

Multiply element $a_{13}$ by its cofactor.

$- 55 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$

Langkah 2.4.3.1.9

Add the terms together.

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 (113 | \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} | - 218 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |) + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.3.2

Evaluasi $| \begin{array}{c} 82 & 106 \\ 143 & 74 \end{array} |$ .

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Langkah 2.4.3.2.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 (113 (82 \cdot 74 - 143 \cdot 106) - 218 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |) + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.3.2.2

Sederhanakan determinannya.

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Langkah 2.4.3.2.2.1

Sederhanakan setiap suku.

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Langkah 2.4.3.2.2.1.1

Kalikan $82$ dengan $74$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 (113 (6068 - 143 \cdot 106) - 218 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |) + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.3.2.2.1.2

Kalikan $- 143$ dengan $106$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 (113 (6068 - 15158) - 218 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |) + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.3.2.2.2

Kurangi $15158$ dengan $6068$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 (113 \cdot - 9090 - 218 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |) + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.3.3

Evaluasi $| \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} |$ .

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Langkah 2.4.3.3.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 (113 \cdot - 9090 - 218 (119 \cdot 74 - 162 \cdot 106) - 55 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |) + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.3.3.2

Sederhanakan determinannya.

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Langkah 2.4.3.3.2.1

Sederhanakan setiap suku.

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Langkah 2.4.3.3.2.1.1

Kalikan $119$ dengan $74$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 (113 \cdot - 9090 - 218 (8806 - 162 \cdot 106) - 55 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |) + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.3.3.2.1.2

Kalikan $- 162$ dengan $106$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 (113 \cdot - 9090 - 218 (8806 - 17172) - 55 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |) + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.3.3.2.2

Kurangi $17172$ dengan $8806$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 (113 \cdot - 9090 - 218 \cdot - 8366 - 55 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |) + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.3.4

Evaluasi $| \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$ .

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Langkah 2.4.3.4.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 (113 \cdot - 9090 - 218 \cdot - 8366 - 55 (119 \cdot 143 - 162 \cdot 82)) + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.3.4.2

Sederhanakan determinannya.

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Langkah 2.4.3.4.2.1

Sederhanakan setiap suku.

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Langkah 2.4.3.4.2.1.1

Kalikan $119$ dengan $143$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 (113 \cdot - 9090 - 218 \cdot - 8366 - 55 (17017 - 162 \cdot 82)) + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.3.4.2.1.2

Kalikan $- 162$ dengan $82$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 (113 \cdot - 9090 - 218 \cdot - 8366 - 55 (17017 - 13284)) + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.3.4.2.2

Kurangi $13284$ dengan $17017$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 (113 \cdot - 9090 - 218 \cdot - 8366 - 55 \cdot 3733) + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.3.5

Sederhanakan determinannya.

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Langkah 2.4.3.5.1

Sederhanakan setiap suku.

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Langkah 2.4.3.5.1.1

Kalikan $113$ dengan $- 9090$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 (- 1027170 - 218 \cdot - 8366 - 55 \cdot 3733) + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.3.5.1.2

Kalikan $- 218$ dengan $- 8366$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 (- 1027170 + 1823788 - 55 \cdot 3733) + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.3.5.1.3

Kalikan $- 55$ dengan $3733$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 (- 1027170 + 1823788 - 205315) + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.3.5.2

Tambahkan $- 1027170$ dan $1823788$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 (796618 - 205315) + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.3.5.3

Kurangi $205315$ dengan $796618$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.4

Evaluasi $| \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} |$ .

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Langkah 2.4.4.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.4.4.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 2.4.4.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.4.4.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} |$

Langkah 2.4.4.1.4

Multiply element $a_{11}$ by its cofactor.

$113 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} |$

Langkah 2.4.4.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} |$

Langkah 2.4.4.1.6

Multiply element $a_{12}$ by its cofactor.

$82 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} |$

Langkah 2.4.4.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$

Langkah 2.4.4.1.8

Multiply element $a_{13}$ by its cofactor.

$- 55 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$

Langkah 2.4.4.1.9

Add the terms together.

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 (113 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | + 82 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.4.2

Evaluasi $| \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} |$ .

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Langkah 2.4.4.2.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 (113 (83 \cdot 74 - 20 \cdot 106) + 82 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.4.2.2

Sederhanakan determinannya.

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Langkah 2.4.4.2.2.1

Sederhanakan setiap suku.

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Langkah 2.4.4.2.2.1.1

Kalikan $83$ dengan $74$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 (113 (6142 - 20 \cdot 106) + 82 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.4.2.2.1.2

Kalikan $- 20$ dengan $106$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 (113 (6142 - 2120) + 82 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.4.2.2.2

Kurangi $2120$ dengan $6142$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 (113 \cdot 4022 + 82 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.4.3

Evaluasi $| \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} |$ .

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Langkah 2.4.4.3.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 (113 \cdot 4022 + 82 (119 \cdot 74 - 162 \cdot 106) - 55 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.4.3.2

Sederhanakan determinannya.

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Langkah 2.4.4.3.2.1

Sederhanakan setiap suku.

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Langkah 2.4.4.3.2.1.1

Kalikan $119$ dengan $74$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 (113 \cdot 4022 + 82 (8806 - 162 \cdot 106) - 55 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.4.3.2.1.2

Kalikan $- 162$ dengan $106$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 (113 \cdot 4022 + 82 (8806 - 17172) - 55 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.4.3.2.2

Kurangi $17172$ dengan $8806$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 (113 \cdot 4022 + 82 \cdot - 8366 - 55 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.4.4

Evaluasi $| \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$ .

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Langkah 2.4.4.4.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 (113 \cdot 4022 + 82 \cdot - 8366 - 55 (119 \cdot 20 - 162 \cdot 83)) - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.4.4.2

Sederhanakan determinannya.

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Langkah 2.4.4.4.2.1

Sederhanakan setiap suku.

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Langkah 2.4.4.4.2.1.1

Kalikan $119$ dengan $20$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 (113 \cdot 4022 + 82 \cdot - 8366 - 55 (2380 - 162 \cdot 83)) - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.4.4.2.1.2

Kalikan $- 162$ dengan $83$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 (113 \cdot 4022 + 82 \cdot - 8366 - 55 (2380 - 13446)) - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.4.4.2.2

Kurangi $13446$ dengan $2380$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 (113 \cdot 4022 + 82 \cdot - 8366 - 55 \cdot - 11066) - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.4.5

Sederhanakan determinannya.

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Langkah 2.4.4.5.1

Sederhanakan setiap suku.

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Langkah 2.4.4.5.1.1

Kalikan $113$ dengan $4022$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 (454486 + 82 \cdot - 8366 - 55 \cdot - 11066) - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.4.5.1.2

Kalikan $82$ dengan $- 8366$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 (454486 - 686012 - 55 \cdot - 11066) - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.4.5.1.3

Kalikan $- 55$ dengan $- 11066$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 (454486 - 686012 + 608630) - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.4.5.2

Kurangi $686012$ dengan $454486$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 (- 231526 + 608630) - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.4.5.3

Tambahkan $- 231526$ dan $608630$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 \cdot 377104 - 105 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.5

Evaluasi $| \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |$ .

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Langkah 2.4.5.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.4.5.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 2.4.5.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.4.5.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |$

Langkah 2.4.5.1.4

Multiply element $a_{11}$ by its cofactor.

$113 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |$

Langkah 2.4.5.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$

Langkah 2.4.5.1.6

Multiply element $a_{12}$ by its cofactor.

$82 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$

Langkah 2.4.5.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$

Langkah 2.4.5.1.8

Multiply element $a_{13}$ by its cofactor.

$218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$

Langkah 2.4.5.1.9

Add the terms together.

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 \cdot 377104 - 105 (113 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} | + 82 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |)) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.5.2

Evaluasi $| \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |$ .

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Langkah 2.4.5.2.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 \cdot 377104 - 105 (113 (83 \cdot 143 - 20 \cdot 82) + 82 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |)) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.5.2.2

Sederhanakan determinannya.

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Langkah 2.4.5.2.2.1

Sederhanakan setiap suku.

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Langkah 2.4.5.2.2.1.1

Kalikan $83$ dengan $143$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 \cdot 377104 - 105 (113 (11869 - 20 \cdot 82) + 82 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |)) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.5.2.2.1.2

Kalikan $- 20$ dengan $82$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 \cdot 377104 - 105 (113 (11869 - 1640) + 82 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |)) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.5.2.2.2

Kurangi $1640$ dengan $11869$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 \cdot 377104 - 105 (113 \cdot 10229 + 82 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |)) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.5.3

Evaluasi $| \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$ .

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Langkah 2.4.5.3.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 \cdot 377104 - 105 (113 \cdot 10229 + 82 (119 \cdot 143 - 162 \cdot 82) + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |)) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.5.3.2

Sederhanakan determinannya.

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Langkah 2.4.5.3.2.1

Sederhanakan setiap suku.

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Langkah 2.4.5.3.2.1.1

Kalikan $119$ dengan $143$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 \cdot 377104 - 105 (113 \cdot 10229 + 82 (17017 - 162 \cdot 82) + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |)) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.5.3.2.1.2

Kalikan $- 162$ dengan $82$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 \cdot 377104 - 105 (113 \cdot 10229 + 82 (17017 - 13284) + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |)) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.5.3.2.2

Kurangi $13284$ dengan $17017$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 \cdot 377104 - 105 (113 \cdot 10229 + 82 \cdot 3733 + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |)) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.5.4

Evaluasi $| \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$ .

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Langkah 2.4.5.4.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 \cdot 377104 - 105 (113 \cdot 10229 + 82 \cdot 3733 + 218 (119 \cdot 20 - 162 \cdot 83))) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.5.4.2

Sederhanakan determinannya.

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Langkah 2.4.5.4.2.1

Sederhanakan setiap suku.

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Langkah 2.4.5.4.2.1.1

Kalikan $119$ dengan $20$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 \cdot 377104 - 105 (113 \cdot 10229 + 82 \cdot 3733 + 218 (2380 - 162 \cdot 83))) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.5.4.2.1.2

Kalikan $- 162$ dengan $83$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 \cdot 377104 - 105 (113 \cdot 10229 + 82 \cdot 3733 + 218 (2380 - 13446))) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.5.4.2.2

Kurangi $13446$ dengan $2380$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 \cdot 377104 - 105 (113 \cdot 10229 + 82 \cdot 3733 + 218 \cdot - 11066)) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.5.5

Sederhanakan determinannya.

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Langkah 2.4.5.5.1

Sederhanakan setiap suku.

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Langkah 2.4.5.5.1.1

Kalikan $113$ dengan $10229$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 \cdot 377104 - 105 (1155877 + 82 \cdot 3733 + 218 \cdot - 11066)) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.5.5.1.2

Kalikan $82$ dengan $3733$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 \cdot 377104 - 105 (1155877 + 306106 + 218 \cdot - 11066)) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.5.5.1.3

Kalikan $218$ dengan $- 11066$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 \cdot 377104 - 105 (1155877 + 306106 - 2412388)) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.5.5.2

Tambahkan $1155877$ dan $306106$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 \cdot 377104 - 105 (1461983 - 2412388)) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.5.5.3

Kurangi $2412388$ dengan $1461983$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (20 \cdot - 694011 - 169 \cdot 591303 + 18 \cdot 377104 - 105 \cdot - 950405) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.6

Sederhanakan determinannya.

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Langkah 2.4.6.1

Sederhanakan setiap suku.

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Langkah 2.4.6.1.1

Kalikan $20$ dengan $- 694011$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (- 13880220 - 169 \cdot 591303 + 18 \cdot 377104 - 105 \cdot - 950405) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.6.1.2

Kalikan $- 169$ dengan $591303$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (- 13880220 - 99930207 + 18 \cdot 377104 - 105 \cdot - 950405) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.6.1.3

Kalikan $18$ dengan $377104$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (- 13880220 - 99930207 + 6787872 - 105 \cdot - 950405) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.6.1.4

Kalikan $- 105$ dengan $- 950405$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (- 13880220 - 99930207 + 6787872 + 99792525) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.6.2

Kurangi $99930207$ dengan $- 13880220$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (- 113810427 + 6787872 + 99792525) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.6.3

Tambahkan $- 113810427$ dan $6787872$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 (- 107022555 + 99792525) + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.4.6.4

Tambahkan $- 107022555$ dan $99792525$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 | \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} | + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5

Evaluasi $| \begin{array}{c} 20 & 169 & - 164 & 105 \\ 113 & - 82 & 239 & - 55 \\ 119 & 83 & 7 & 106 \\ 162 & 20 & 175 & 74 \end{array} |$ .

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Langkah 2.5.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.5.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + & - \\ - & + & - & + \\ + & - & + & - \\ - & + & - & + \end{array} |$

Langkah 2.5.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.5.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} |$

Langkah 2.5.1.4

Multiply element $a_{11}$ by its cofactor.

$20 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} |$

Langkah 2.5.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} |$

Langkah 2.5.1.6

Multiply element $a_{12}$ by its cofactor.

$- 169 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} |$

Langkah 2.5.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} |$

Langkah 2.5.1.8

Multiply element $a_{13}$ by its cofactor.

$- 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} |$

Langkah 2.5.1.9

The minor for $a_{14}$ is the determinant with row $1$ and column $4$ deleted.

$| \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |$

Langkah 2.5.1.10

Multiply element $a_{14}$ by its cofactor.

$- 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |$

Langkah 2.5.1.11

Add the terms together.

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 | \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} | - 169 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.2

Evaluasi $| \begin{array}{c} - 82 & 239 & - 55 \\ 83 & 7 & 106 \\ 20 & 175 & 74 \end{array} |$ .

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Langkah 2.5.2.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.5.2.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 2.5.2.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.5.2.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} |$

Langkah 2.5.2.1.4

Multiply element $a_{11}$ by its cofactor.

$- 82 | \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} |$

Langkah 2.5.2.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} |$

Langkah 2.5.2.1.6

Multiply element $a_{12}$ by its cofactor.

$- 239 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} |$

Langkah 2.5.2.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$

Langkah 2.5.2.1.8

Multiply element $a_{13}$ by its cofactor.

$- 55 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$

Langkah 2.5.2.1.9

Add the terms together.

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 (- 82 | \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} | - 239 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | - 55 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.2.2

Evaluasi $| \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} |$ .

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Langkah 2.5.2.2.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 (- 82 (7 \cdot 74 - 175 \cdot 106) - 239 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | - 55 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.2.2.2

Sederhanakan determinannya.

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Langkah 2.5.2.2.2.1

Sederhanakan setiap suku.

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Langkah 2.5.2.2.2.1.1

Kalikan $7$ dengan $74$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 (- 82 (518 - 175 \cdot 106) - 239 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | - 55 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.2.2.2.1.2

Kalikan $- 175$ dengan $106$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 (- 82 (518 - 18550) - 239 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | - 55 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.2.2.2.2

Kurangi $18550$ dengan $518$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 (- 82 \cdot - 18032 - 239 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | - 55 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.2.3

Evaluasi $| \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} |$ .

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Langkah 2.5.2.3.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 (- 82 \cdot - 18032 - 239 (83 \cdot 74 - 20 \cdot 106) - 55 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.2.3.2

Sederhanakan determinannya.

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Langkah 2.5.2.3.2.1

Sederhanakan setiap suku.

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Langkah 2.5.2.3.2.1.1

Kalikan $83$ dengan $74$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 (- 82 \cdot - 18032 - 239 (6142 - 20 \cdot 106) - 55 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.2.3.2.1.2

Kalikan $- 20$ dengan $106$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 (- 82 \cdot - 18032 - 239 (6142 - 2120) - 55 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.2.3.2.2

Kurangi $2120$ dengan $6142$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 (- 82 \cdot - 18032 - 239 \cdot 4022 - 55 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.2.4

Evaluasi $| \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$ .

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Langkah 2.5.2.4.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 (- 82 \cdot - 18032 - 239 \cdot 4022 - 55 (83 \cdot 175 - 20 \cdot 7)) - 169 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.2.4.2

Sederhanakan determinannya.

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Langkah 2.5.2.4.2.1

Sederhanakan setiap suku.

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Langkah 2.5.2.4.2.1.1

Kalikan $83$ dengan $175$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 (- 82 \cdot - 18032 - 239 \cdot 4022 - 55 (14525 - 20 \cdot 7)) - 169 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.2.4.2.1.2

Kalikan $- 20$ dengan $7$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 (- 82 \cdot - 18032 - 239 \cdot 4022 - 55 (14525 - 140)) - 169 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.2.4.2.2

Kurangi $140$ dengan $14525$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 (- 82 \cdot - 18032 - 239 \cdot 4022 - 55 \cdot 14385) - 169 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.2.5

Sederhanakan determinannya.

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Langkah 2.5.2.5.1

Sederhanakan setiap suku.

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Langkah 2.5.2.5.1.1

Kalikan $- 82$ dengan $- 18032$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 (1478624 - 239 \cdot 4022 - 55 \cdot 14385) - 169 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.2.5.1.2

Kalikan $- 239$ dengan $4022$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 (1478624 - 961258 - 55 \cdot 14385) - 169 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.2.5.1.3

Kalikan $- 55$ dengan $14385$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 (1478624 - 961258 - 791175) - 169 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.2.5.2

Kurangi $961258$ dengan $1478624$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 (517366 - 791175) - 169 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.2.5.3

Kurangi $791175$ dengan $517366$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 | \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.3

Evaluasi $| \begin{array}{c} 113 & 239 & - 55 \\ 119 & 7 & 106 \\ 162 & 175 & 74 \end{array} |$ .

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Langkah 2.5.3.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.5.3.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 2.5.3.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.5.3.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} |$

Langkah 2.5.3.1.4

Multiply element $a_{11}$ by its cofactor.

$113 | \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} |$

Langkah 2.5.3.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} |$

Langkah 2.5.3.1.6

Multiply element $a_{12}$ by its cofactor.

$- 239 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} |$

Langkah 2.5.3.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$

Langkah 2.5.3.1.8

Multiply element $a_{13}$ by its cofactor.

$- 55 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$

Langkah 2.5.3.1.9

Add the terms together.

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 (113 | \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} | - 239 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.3.2

Evaluasi $| \begin{array}{c} 7 & 106 \\ 175 & 74 \end{array} |$ .

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Langkah 2.5.3.2.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 (113 (7 \cdot 74 - 175 \cdot 106) - 239 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.3.2.2

Sederhanakan determinannya.

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Langkah 2.5.3.2.2.1

Sederhanakan setiap suku.

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Langkah 2.5.3.2.2.1.1

Kalikan $7$ dengan $74$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 (113 (518 - 175 \cdot 106) - 239 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.3.2.2.1.2

Kalikan $- 175$ dengan $106$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 (113 (518 - 18550) - 239 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.3.2.2.2

Kurangi $18550$ dengan $518$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 (113 \cdot - 18032 - 239 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.3.3

Evaluasi $| \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} |$ .

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Langkah 2.5.3.3.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 (113 \cdot - 18032 - 239 (119 \cdot 74 - 162 \cdot 106) - 55 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.3.3.2

Sederhanakan determinannya.

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Langkah 2.5.3.3.2.1

Sederhanakan setiap suku.

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Langkah 2.5.3.3.2.1.1

Kalikan $119$ dengan $74$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 (113 \cdot - 18032 - 239 (8806 - 162 \cdot 106) - 55 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.3.3.2.1.2

Kalikan $- 162$ dengan $106$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 (113 \cdot - 18032 - 239 (8806 - 17172) - 55 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.3.3.2.2

Kurangi $17172$ dengan $8806$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 (113 \cdot - 18032 - 239 \cdot - 8366 - 55 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.3.4

Evaluasi $| \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$ .

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Langkah 2.5.3.4.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 (113 \cdot - 18032 - 239 \cdot - 8366 - 55 (119 \cdot 175 - 162 \cdot 7)) - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.3.4.2

Sederhanakan determinannya.

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Langkah 2.5.3.4.2.1

Sederhanakan setiap suku.

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Langkah 2.5.3.4.2.1.1

Kalikan $119$ dengan $175$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 (113 \cdot - 18032 - 239 \cdot - 8366 - 55 (20825 - 162 \cdot 7)) - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.3.4.2.1.2

Kalikan $- 162$ dengan $7$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 (113 \cdot - 18032 - 239 \cdot - 8366 - 55 (20825 - 1134)) - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.3.4.2.2

Kurangi $1134$ dengan $20825$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 (113 \cdot - 18032 - 239 \cdot - 8366 - 55 \cdot 19691) - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.3.5

Sederhanakan determinannya.

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Langkah 2.5.3.5.1

Sederhanakan setiap suku.

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Langkah 2.5.3.5.1.1

Kalikan $113$ dengan $- 18032$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 (- 2037616 - 239 \cdot - 8366 - 55 \cdot 19691) - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.3.5.1.2

Kalikan $- 239$ dengan $- 8366$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 (- 2037616 + 1999474 - 55 \cdot 19691) - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.3.5.1.3

Kalikan $- 55$ dengan $19691$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 (- 2037616 + 1999474 - 1083005) - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.3.5.2

Tambahkan $- 2037616$ dan $1999474$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 (- 38142 - 1083005) - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.3.5.3

Kurangi $1083005$ dengan $- 38142$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 | \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} | - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.4

Evaluasi $| \begin{array}{c} 113 & - 82 & - 55 \\ 119 & 83 & 106 \\ 162 & 20 & 74 \end{array} |$ .

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Langkah 2.5.4.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.5.4.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 2.5.4.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.5.4.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} |$

Langkah 2.5.4.1.4

Multiply element $a_{11}$ by its cofactor.

$113 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} |$

Langkah 2.5.4.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} |$

Langkah 2.5.4.1.6

Multiply element $a_{12}$ by its cofactor.

$82 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} |$

Langkah 2.5.4.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$

Langkah 2.5.4.1.8

Multiply element $a_{13}$ by its cofactor.

$- 55 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$

Langkah 2.5.4.1.9

Add the terms together.

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 (113 | \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} | + 82 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.4.2

Evaluasi $| \begin{array}{c} 83 & 106 \\ 20 & 74 \end{array} |$ .

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Langkah 2.5.4.2.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 (113 (83 \cdot 74 - 20 \cdot 106) + 82 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.4.2.2

Sederhanakan determinannya.

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Langkah 2.5.4.2.2.1

Sederhanakan setiap suku.

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Langkah 2.5.4.2.2.1.1

Kalikan $83$ dengan $74$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 (113 (6142 - 20 \cdot 106) + 82 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.4.2.2.1.2

Kalikan $- 20$ dengan $106$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 (113 (6142 - 2120) + 82 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.4.2.2.2

Kurangi $2120$ dengan $6142$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 (113 \cdot 4022 + 82 | \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} | - 55 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.4.3

Evaluasi $| \begin{array}{c} 119 & 106 \\ 162 & 74 \end{array} |$ .

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Langkah 2.5.4.3.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 (113 \cdot 4022 + 82 (119 \cdot 74 - 162 \cdot 106) - 55 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.4.3.2

Sederhanakan determinannya.

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Langkah 2.5.4.3.2.1

Sederhanakan setiap suku.

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Langkah 2.5.4.3.2.1.1

Kalikan $119$ dengan $74$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 (113 \cdot 4022 + 82 (8806 - 162 \cdot 106) - 55 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.4.3.2.1.2

Kalikan $- 162$ dengan $106$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 (113 \cdot 4022 + 82 (8806 - 17172) - 55 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.4.3.2.2

Kurangi $17172$ dengan $8806$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 (113 \cdot 4022 + 82 \cdot - 8366 - 55 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.4.4

Evaluasi $| \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$ .

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Langkah 2.5.4.4.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 (113 \cdot 4022 + 82 \cdot - 8366 - 55 (119 \cdot 20 - 162 \cdot 83)) - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.4.4.2

Sederhanakan determinannya.

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Langkah 2.5.4.4.2.1

Sederhanakan setiap suku.

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Langkah 2.5.4.4.2.1.1

Kalikan $119$ dengan $20$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 (113 \cdot 4022 + 82 \cdot - 8366 - 55 (2380 - 162 \cdot 83)) - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.4.4.2.1.2

Kalikan $- 162$ dengan $83$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 (113 \cdot 4022 + 82 \cdot - 8366 - 55 (2380 - 13446)) - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.4.4.2.2

Kurangi $13446$ dengan $2380$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 (113 \cdot 4022 + 82 \cdot - 8366 - 55 \cdot - 11066) - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.4.5

Sederhanakan determinannya.

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Langkah 2.5.4.5.1

Sederhanakan setiap suku.

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Langkah 2.5.4.5.1.1

Kalikan $113$ dengan $4022$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 (454486 + 82 \cdot - 8366 - 55 \cdot - 11066) - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.4.5.1.2

Kalikan $82$ dengan $- 8366$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 (454486 - 686012 - 55 \cdot - 11066) - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.4.5.1.3

Kalikan $- 55$ dengan $- 11066$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 (454486 - 686012 + 608630) - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.4.5.2

Kurangi $686012$ dengan $454486$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 (- 231526 + 608630) - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.4.5.3

Tambahkan $- 231526$ dan $608630$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 \cdot 377104 - 105 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.5

Evaluasi $| \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |$ .

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Langkah 2.5.5.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.5.5.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 2.5.5.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.5.5.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$

Langkah 2.5.5.1.4

Multiply element $a_{11}$ by its cofactor.

$113 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$

Langkah 2.5.5.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$

Langkah 2.5.5.1.6

Multiply element $a_{12}$ by its cofactor.

$82 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$

Langkah 2.5.5.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$

Langkah 2.5.5.1.8

Multiply element $a_{13}$ by its cofactor.

$239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$

Langkah 2.5.5.1.9

Add the terms together.

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 \cdot 377104 - 105 (113 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} | + 82 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} | + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |)) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.5.2

Evaluasi $| \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$ .

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Langkah 2.5.5.2.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 \cdot 377104 - 105 (113 (83 \cdot 175 - 20 \cdot 7) + 82 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} | + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |)) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.5.2.2

Sederhanakan determinannya.

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Langkah 2.5.5.2.2.1

Sederhanakan setiap suku.

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Langkah 2.5.5.2.2.1.1

Kalikan $83$ dengan $175$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 \cdot 377104 - 105 (113 (14525 - 20 \cdot 7) + 82 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} | + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |)) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.5.2.2.1.2

Kalikan $- 20$ dengan $7$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 \cdot 377104 - 105 (113 (14525 - 140) + 82 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} | + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |)) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.5.2.2.2

Kurangi $140$ dengan $14525$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 \cdot 377104 - 105 (113 \cdot 14385 + 82 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} | + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |)) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.5.3

Evaluasi $| \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$ .

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Langkah 2.5.5.3.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 \cdot 377104 - 105 (113 \cdot 14385 + 82 (119 \cdot 175 - 162 \cdot 7) + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |)) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.5.3.2

Sederhanakan determinannya.

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Langkah 2.5.5.3.2.1

Sederhanakan setiap suku.

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Langkah 2.5.5.3.2.1.1

Kalikan $119$ dengan $175$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 \cdot 377104 - 105 (113 \cdot 14385 + 82 (20825 - 162 \cdot 7) + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |)) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.5.3.2.1.2

Kalikan $- 162$ dengan $7$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 \cdot 377104 - 105 (113 \cdot 14385 + 82 (20825 - 1134) + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |)) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.5.3.2.2

Kurangi $1134$ dengan $20825$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 \cdot 377104 - 105 (113 \cdot 14385 + 82 \cdot 19691 + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |)) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.5.4

Evaluasi $| \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$ .

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Langkah 2.5.5.4.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 \cdot 377104 - 105 (113 \cdot 14385 + 82 \cdot 19691 + 239 (119 \cdot 20 - 162 \cdot 83))) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.5.4.2

Sederhanakan determinannya.

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Langkah 2.5.5.4.2.1

Sederhanakan setiap suku.

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Langkah 2.5.5.4.2.1.1

Kalikan $119$ dengan $20$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 \cdot 377104 - 105 (113 \cdot 14385 + 82 \cdot 19691 + 239 (2380 - 162 \cdot 83))) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.5.4.2.1.2

Kalikan $- 162$ dengan $83$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 \cdot 377104 - 105 (113 \cdot 14385 + 82 \cdot 19691 + 239 (2380 - 13446))) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.5.4.2.2

Kurangi $13446$ dengan $2380$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 \cdot 377104 - 105 (113 \cdot 14385 + 82 \cdot 19691 + 239 \cdot - 11066)) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.5.5

Sederhanakan determinannya.

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Langkah 2.5.5.5.1

Sederhanakan setiap suku.

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Langkah 2.5.5.5.1.1

Kalikan $113$ dengan $14385$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 \cdot 377104 - 105 (1625505 + 82 \cdot 19691 + 239 \cdot - 11066)) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.5.5.1.2

Kalikan $82$ dengan $19691$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 \cdot 377104 - 105 (1625505 + 1614662 + 239 \cdot - 11066)) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.5.5.1.3

Kalikan $239$ dengan $- 11066$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 \cdot 377104 - 105 (1625505 + 1614662 - 2644774)) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.5.5.2

Tambahkan $1625505$ dan $1614662$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 \cdot 377104 - 105 (3240167 - 2644774)) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.5.5.3

Kurangi $2644774$ dengan $3240167$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (20 \cdot - 273809 - 169 \cdot - 1121147 - 164 \cdot 377104 - 105 \cdot 595393) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.6

Sederhanakan determinannya.

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Langkah 2.5.6.1

Sederhanakan setiap suku.

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Langkah 2.5.6.1.1

Kalikan $20$ dengan $- 273809$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (- 5476180 - 169 \cdot - 1121147 - 164 \cdot 377104 - 105 \cdot 595393) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.6.1.2

Kalikan $- 169$ dengan $- 1121147$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (- 5476180 + 189473843 - 164 \cdot 377104 - 105 \cdot 595393) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.6.1.3

Kalikan $- 164$ dengan $377104$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (- 5476180 + 189473843 - 61845056 - 105 \cdot 595393) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.6.1.4

Kalikan $- 105$ dengan $595393$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (- 5476180 + 189473843 - 61845056 - 62516265) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.6.2

Tambahkan $- 5476180$ dan $189473843$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (183997663 - 61845056 - 62516265) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.6.3

Kurangi $61845056$ dengan $183997663$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 (122152607 - 62516265) + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.5.6.4

Kurangi $62516265$ dengan $122152607$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 | \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$

Langkah 2.6

Evaluasi $| \begin{array}{c} 20 & 169 & - 164 & 18 \\ 113 & - 82 & 239 & 218 \\ 119 & 83 & 7 & 82 \\ 162 & 20 & 175 & 143 \end{array} |$ .

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Langkah 2.6.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.6.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + & - \\ - & + & - & + \\ + & - & + & - \\ - & + & - & + \end{array} |$

Langkah 2.6.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.6.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |$

Langkah 2.6.1.4

Multiply element $a_{11}$ by its cofactor.

$20 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |$

Langkah 2.6.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |$

Langkah 2.6.1.6

Multiply element $a_{12}$ by its cofactor.

$- 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |$

Langkah 2.6.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |$

Langkah 2.6.1.8

Multiply element $a_{13}$ by its cofactor.

$- 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |$

Langkah 2.6.1.9

The minor for $a_{14}$ is the determinant with row $1$ and column $4$ deleted.

$| \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |$

Langkah 2.6.1.10

Multiply element $a_{14}$ by its cofactor.

$- 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |$

Langkah 2.6.1.11

Add the terms together.

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 | \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} | - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.2

Evaluasi $| \begin{array}{c} - 82 & 239 & 218 \\ 83 & 7 & 82 \\ 20 & 175 & 143 \end{array} |$ .

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Langkah 2.6.2.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.6.2.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 2.6.2.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.6.2.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |$

Langkah 2.6.2.1.4

Multiply element $a_{11}$ by its cofactor.

$- 82 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |$

Langkah 2.6.2.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |$

Langkah 2.6.2.1.6

Multiply element $a_{12}$ by its cofactor.

$- 239 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |$

Langkah 2.6.2.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$

Langkah 2.6.2.1.8

Multiply element $a_{13}$ by its cofactor.

$218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$

Langkah 2.6.2.1.9

Add the terms together.

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} | - 239 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} | + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.2.2

Evaluasi $| \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |$ .

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Langkah 2.6.2.2.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 (7 \cdot 143 - 175 \cdot 82) - 239 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} | + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.2.2.2

Sederhanakan determinannya.

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Langkah 2.6.2.2.2.1

Sederhanakan setiap suku.

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Langkah 2.6.2.2.2.1.1

Kalikan $7$ dengan $143$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 (1001 - 175 \cdot 82) - 239 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} | + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.2.2.2.1.2

Kalikan $- 175$ dengan $82$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 (1001 - 14350) - 239 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} | + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.2.2.2.2

Kurangi $14350$ dengan $1001$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 \cdot - 13349 - 239 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} | + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.2.3

Evaluasi $| \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |$ .

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Langkah 2.6.2.3.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 \cdot - 13349 - 239 (83 \cdot 143 - 20 \cdot 82) + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.2.3.2

Sederhanakan determinannya.

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Langkah 2.6.2.3.2.1

Sederhanakan setiap suku.

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Langkah 2.6.2.3.2.1.1

Kalikan $83$ dengan $143$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 \cdot - 13349 - 239 (11869 - 20 \cdot 82) + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.2.3.2.1.2

Kalikan $- 20$ dengan $82$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 \cdot - 13349 - 239 (11869 - 1640) + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.2.3.2.2

Kurangi $1640$ dengan $11869$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 \cdot - 13349 - 239 \cdot 10229 + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.2.4

Evaluasi $| \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$ .

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Langkah 2.6.2.4.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 \cdot - 13349 - 239 \cdot 10229 + 218 (83 \cdot 175 - 20 \cdot 7)) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.2.4.2

Sederhanakan determinannya.

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Langkah 2.6.2.4.2.1

Sederhanakan setiap suku.

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Langkah 2.6.2.4.2.1.1

Kalikan $83$ dengan $175$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 \cdot - 13349 - 239 \cdot 10229 + 218 (14525 - 20 \cdot 7)) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.2.4.2.1.2

Kalikan $- 20$ dengan $7$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 \cdot - 13349 - 239 \cdot 10229 + 218 (14525 - 140)) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.2.4.2.2

Kurangi $140$ dengan $14525$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 \cdot - 13349 - 239 \cdot 10229 + 218 \cdot 14385) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.2.5

Sederhanakan determinannya.

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Langkah 2.6.2.5.1

Sederhanakan setiap suku.

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Langkah 2.6.2.5.1.1

Kalikan $- 82$ dengan $- 13349$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (1094618 - 239 \cdot 10229 + 218 \cdot 14385) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.2.5.1.2

Kalikan $- 239$ dengan $10229$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (1094618 - 2444731 + 218 \cdot 14385) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.2.5.1.3

Kalikan $218$ dengan $14385$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (1094618 - 2444731 + 3135930) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.2.5.2

Kurangi $2444731$ dengan $1094618$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 1350113 + 3135930) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.2.5.3

Tambahkan $- 1350113$ dan $3135930$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.3

Evaluasi $| \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} |$ .

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Langkah 2.6.3.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.6.3.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 2.6.3.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.6.3.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |$

Langkah 2.6.3.1.4

Multiply element $a_{11}$ by its cofactor.

$113 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |$

Langkah 2.6.3.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$

Langkah 2.6.3.1.6

Multiply element $a_{12}$ by its cofactor.

$- 239 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$

Langkah 2.6.3.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$

Langkah 2.6.3.1.8

Multiply element $a_{13}$ by its cofactor.

$218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$

Langkah 2.6.3.1.9

Add the terms together.

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} | - 239 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.3.2

Evaluasi $| \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} |$ .

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Langkah 2.6.3.2.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 (7 \cdot 143 - 175 \cdot 82) - 239 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.3.2.2

Sederhanakan determinannya.

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Langkah 2.6.3.2.2.1

Sederhanakan setiap suku.

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Langkah 2.6.3.2.2.1.1

Kalikan $7$ dengan $143$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 (1001 - 175 \cdot 82) - 239 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.3.2.2.1.2

Kalikan $- 175$ dengan $82$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 (1001 - 14350) - 239 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.3.2.2.2

Kurangi $14350$ dengan $1001$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 \cdot - 13349 - 239 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.3.3

Evaluasi $| \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$ .

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Langkah 2.6.3.3.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 \cdot - 13349 - 239 (119 \cdot 143 - 162 \cdot 82) + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.3.3.2

Sederhanakan determinannya.

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Langkah 2.6.3.3.2.1

Sederhanakan setiap suku.

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Langkah 2.6.3.3.2.1.1

Kalikan $119$ dengan $143$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 \cdot - 13349 - 239 (17017 - 162 \cdot 82) + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.3.3.2.1.2

Kalikan $- 162$ dengan $82$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 \cdot - 13349 - 239 (17017 - 13284) + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.3.3.2.2

Kurangi $13284$ dengan $17017$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 \cdot - 13349 - 239 \cdot 3733 + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.3.4

Evaluasi $| \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$ .

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Langkah 2.6.3.4.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 \cdot - 13349 - 239 \cdot 3733 + 218 (119 \cdot 175 - 162 \cdot 7)) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.3.4.2

Sederhanakan determinannya.

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Langkah 2.6.3.4.2.1

Sederhanakan setiap suku.

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Langkah 2.6.3.4.2.1.1

Kalikan $119$ dengan $175$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 \cdot - 13349 - 239 \cdot 3733 + 218 (20825 - 162 \cdot 7)) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.3.4.2.1.2

Kalikan $- 162$ dengan $7$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 \cdot - 13349 - 239 \cdot 3733 + 218 (20825 - 1134)) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.3.4.2.2

Kurangi $1134$ dengan $20825$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 \cdot - 13349 - 239 \cdot 3733 + 218 \cdot 19691) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.3.5

Sederhanakan determinannya.

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Langkah 2.6.3.5.1

Sederhanakan setiap suku.

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Langkah 2.6.3.5.1.1

Kalikan $113$ dengan $- 13349$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (- 1508437 - 239 \cdot 3733 + 218 \cdot 19691) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.3.5.1.2

Kalikan $- 239$ dengan $3733$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (- 1508437 - 892187 + 218 \cdot 19691) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.3.5.1.3

Kalikan $218$ dengan $19691$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (- 1508437 - 892187 + 4292638) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.3.5.2

Kurangi $892187$ dengan $- 1508437$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (- 2400624 + 4292638) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.3.5.3

Tambahkan $- 2400624$ dan $4292638$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.4

Evaluasi $| \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} |$ .

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Langkah 2.6.4.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.6.4.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 2.6.4.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.6.4.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |$

Langkah 2.6.4.1.4

Multiply element $a_{11}$ by its cofactor.

$113 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |$

Langkah 2.6.4.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$

Langkah 2.6.4.1.6

Multiply element $a_{12}$ by its cofactor.

$82 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$

Langkah 2.6.4.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$

Langkah 2.6.4.1.8

Multiply element $a_{13}$ by its cofactor.

$218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$

Langkah 2.6.4.1.9

Add the terms together.

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} | + 82 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.4.2

Evaluasi $| \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |$ .

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Langkah 2.6.4.2.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 (83 \cdot 143 - 20 \cdot 82) + 82 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.4.2.2

Sederhanakan determinannya.

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Langkah 2.6.4.2.2.1

Sederhanakan setiap suku.

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Langkah 2.6.4.2.2.1.1

Kalikan $83$ dengan $143$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 (11869 - 20 \cdot 82) + 82 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.4.2.2.1.2

Kalikan $- 20$ dengan $82$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 (11869 - 1640) + 82 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.4.2.2.2

Kurangi $1640$ dengan $11869$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 \cdot 10229 + 82 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.4.3

Evaluasi $| \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$ .

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Langkah 2.6.4.3.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 \cdot 10229 + 82 (119 \cdot 143 - 162 \cdot 82) + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.4.3.2

Sederhanakan determinannya.

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Langkah 2.6.4.3.2.1

Sederhanakan setiap suku.

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Langkah 2.6.4.3.2.1.1

Kalikan $119$ dengan $143$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 \cdot 10229 + 82 (17017 - 162 \cdot 82) + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.4.3.2.1.2

Kalikan $- 162$ dengan $82$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 \cdot 10229 + 82 (17017 - 13284) + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.4.3.2.2

Kurangi $13284$ dengan $17017$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 \cdot 10229 + 82 \cdot 3733 + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.4.4

Evaluasi $| \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$ .

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Langkah 2.6.4.4.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 \cdot 10229 + 82 \cdot 3733 + 218 (119 \cdot 20 - 162 \cdot 83)) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.4.4.2

Sederhanakan determinannya.

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Langkah 2.6.4.4.2.1

Sederhanakan setiap suku.

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Langkah 2.6.4.4.2.1.1

Kalikan $119$ dengan $20$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 \cdot 10229 + 82 \cdot 3733 + 218 (2380 - 162 \cdot 83)) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.4.4.2.1.2

Kalikan $- 162$ dengan $83$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 \cdot 10229 + 82 \cdot 3733 + 218 (2380 - 13446)) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.4.4.2.2

Kurangi $13446$ dengan $2380$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 \cdot 10229 + 82 \cdot 3733 + 218 \cdot - 11066) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.4.5

Sederhanakan determinannya.

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Langkah 2.6.4.5.1

Sederhanakan setiap suku.

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Langkah 2.6.4.5.1.1

Kalikan $113$ dengan $10229$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (1155877 + 82 \cdot 3733 + 218 \cdot - 11066) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.4.5.1.2

Kalikan $82$ dengan $3733$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (1155877 + 306106 + 218 \cdot - 11066) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.4.5.1.3

Kalikan $218$ dengan $- 11066$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (1155877 + 306106 - 2412388) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.4.5.2

Tambahkan $1155877$ dan $306106$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (1461983 - 2412388) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.4.5.3

Kurangi $2412388$ dengan $1461983$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Langkah 2.6.5

Evaluasi $| \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |$ .

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Langkah 2.6.5.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Langkah 2.6.5.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 2.6.5.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 2.6.5.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$

Langkah 2.6.5.1.4

Multiply element $a_{11}$ by its cofactor.

$113 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$

Langkah 2.6.5.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$

Langkah 2.6.5.1.6

Multiply element $a_{12}$ by its cofactor.

$82 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$

Langkah 2.6.5.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$

Langkah 2.6.5.1.8

Multiply element $a_{13}$ by its cofactor.

$239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$

Langkah 2.6.5.1.9

Add the terms together.

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (113 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} | + 82 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} | + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |))$

Langkah 2.6.5.2

Evaluasi $| \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$ .

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Langkah 2.6.5.2.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (113 (83 \cdot 175 - 20 \cdot 7) + 82 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} | + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |))$

Langkah 2.6.5.2.2

Sederhanakan determinannya.

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Langkah 2.6.5.2.2.1

Sederhanakan setiap suku.

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Langkah 2.6.5.2.2.1.1

Kalikan $83$ dengan $175$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (113 (14525 - 20 \cdot 7) + 82 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} | + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |))$

Langkah 2.6.5.2.2.1.2

Kalikan $- 20$ dengan $7$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (113 (14525 - 140) + 82 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} | + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |))$

Langkah 2.6.5.2.2.2

Kurangi $140$ dengan $14525$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (113 \cdot 14385 + 82 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} | + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |))$

Langkah 2.6.5.3

Evaluasi $| \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$ .

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Langkah 2.6.5.3.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (113 \cdot 14385 + 82 (119 \cdot 175 - 162 \cdot 7) + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |))$

Langkah 2.6.5.3.2

Sederhanakan determinannya.

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Langkah 2.6.5.3.2.1

Sederhanakan setiap suku.

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Langkah 2.6.5.3.2.1.1

Kalikan $119$ dengan $175$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (113 \cdot 14385 + 82 (20825 - 162 \cdot 7) + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |))$

Langkah 2.6.5.3.2.1.2

Kalikan $- 162$ dengan $7$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (113 \cdot 14385 + 82 (20825 - 1134) + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |))$

Langkah 2.6.5.3.2.2

Kurangi $1134$ dengan $20825$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (113 \cdot 14385 + 82 \cdot 19691 + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |))$

Langkah 2.6.5.4

Evaluasi $| \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$ .

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Langkah 2.6.5.4.1

Determinan dari matriks $2 \times 2$ dapat dicari menggunakan rumus $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

Langkah 2.6.5.4.2

Sederhanakan determinannya.

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Langkah 2.6.5.4.2.1

Sederhanakan setiap suku.

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Langkah 2.6.5.4.2.1.1

Kalikan $119$ dengan $20$ .

Langkah 2.6.5.4.2.1.2

Kalikan $- 162$ dengan $83$ .

Langkah 2.6.5.4.2.2

Kurangi $13446$ dengan $2380$ .

Langkah 2.6.5.5

Sederhanakan determinannya.

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Langkah 2.6.5.5.1

Sederhanakan setiap suku.

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Langkah 2.6.5.5.1.1

Kalikan $113$ dengan $14385$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (1625505 + 82 \cdot 19691 + 239 \cdot - 11066))$

Langkah 2.6.5.5.1.2

Kalikan $82$ dengan $19691$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (1625505 + 1614662 + 239 \cdot - 11066))$

Langkah 2.6.5.5.1.3

Kalikan $239$ dengan $- 11066$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (1625505 + 1614662 - 2644774))$

Langkah 2.6.5.5.2

Tambahkan $1625505$ dan $1614662$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (3240167 - 2644774))$

Langkah 2.6.5.5.3

Kurangi $2644774$ dengan $3240167$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 \cdot 595393)$

Langkah 2.6.6

Sederhanakan determinannya.

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Langkah 2.6.6.1

Sederhanakan setiap suku.

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Langkah 2.6.6.1.1

Kalikan $20$ dengan $1785817$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (35716340 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 \cdot 595393)$

Langkah 2.6.6.1.2

Kalikan $- 169$ dengan $1892014$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (35716340 - 319750366 - 164 \cdot - 950405 - 18 \cdot 595393)$

Langkah 2.6.6.1.3

Kalikan $- 164$ dengan $- 950405$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (35716340 - 319750366 + 155866420 - 18 \cdot 595393)$

Langkah 2.6.6.1.4

Kalikan $- 18$ dengan $595393$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (35716340 - 319750366 + 155866420 - 10717074)$

Langkah 2.6.6.2

Kurangi $319750366$ dengan $35716340$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (- 284034026 + 155866420 - 10717074)$

Langkah 2.6.6.3

Tambahkan $- 284034026$ dan $155866420$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (- 128167606 - 10717074)$

Langkah 2.6.6.4

Kurangi $10717074$ dengan $- 128167606$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 \cdot - 138884680$

Langkah 2.7

Sederhanakan determinannya.

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Langkah 2.7.1

Sederhanakan setiap suku.

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Langkah 2.7.1.1

Kalikan $44$ dengan $115002558$ .

$5060112552 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 \cdot - 138884680$

Langkah 2.7.1.2

Kalikan $- 75$ dengan $- 72015204$ .

$5060112552 + 5401140300 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 \cdot - 138884680$

Langkah 2.7.1.3

Kalikan $- 60$ dengan $- 7230030$ .

$5060112552 + 5401140300 + 433801800 + 33 \cdot 59636342 + 11 \cdot - 138884680$

Langkah 2.7.1.4

Kalikan $33$ dengan $59636342$ .

$5060112552 + 5401140300 + 433801800 + 1967999286 + 11 \cdot - 138884680$

Langkah 2.7.1.5

Kalikan $11$ dengan $- 138884680$ .

$5060112552 + 5401140300 + 433801800 + 1967999286 - 1527731480$

Langkah 2.7.2

Tambahkan $5060112552$ dan $5401140300$ .

$10461252852 + 433801800 + 1967999286 - 1527731480$

Langkah 2.7.3

Tambahkan $10461252852$ dan $433801800$ .

$10895054652 + 1967999286 - 1527731480$

Langkah 2.7.4

Tambahkan $10895054652$ dan $1967999286$ .

$12863053938 - 1527731480$

Langkah 2.7.5

Kurangi $1527731480$ dengan $12863053938$ .

$11335322458$

Langkah 3

Since the determinant is non-zero, the inverse exists.

Langkah 4

Set up a $5 \times 10$ matrix where the left half is the original matrix and the right half is its identity matrix.

$[\begin{array}{c} 44 & 75 & - 60 & - 33 & 11 & 1 & 0 & 0 & 0 & 0 \\ 20 & 169 & - 164 & 18 & 105 & 0 & 1 & 0 & 0 & 0 \\ 113 & - 82 & 239 & 218 & - 55 & 0 & 0 & 1 & 0 & 0 \\ 119 & 83 & 7 & 82 & 106 & 0 & 0 & 0 & 1 & 0 \\ 162 & 20 & 175 & 143 & 74 & 0 & 0 & 0 & 0 & 1 \end{array}]$

Langkah 5

Tentukan bentuk eselon baris yang dikurangi.

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Langkah 5.1

Multiply each element of $R_{1}$ by $\frac{1}{44}$ to make the entry at $1, 1$ a $1$ .

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Langkah 5.1.1

Multiply each element of $R_{1}$ by $\frac{1}{44}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{44}{44} & \frac{75}{44} & \frac{- 60}{44} & \frac{- 33}{44} & \frac{11}{44} & \frac{1}{44} & \frac{0}{44} & \frac{0}{44} & \frac{0}{44} & \frac{0}{44} \\ 20 & 169 & - 164 & 18 & 105 & 0 & 1 & 0 & 0 & 0 \\ 113 & - 82 & 239 & 218 & - 55 & 0 & 0 & 1 & 0 & 0 \\ 119 & 83 & 7 & 82 & 106 & 0 & 0 & 0 & 1 & 0 \\ 162 & 20 & 175 & 143 & 74 & 0 & 0 & 0 & 0 & 1 \end{array}]$

Langkah 5.1.2

Sederhanakan $R_{1}$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 20 & 169 & - 164 & 18 & 105 & 0 & 1 & 0 & 0 & 0 \\ 113 & - 82 & 239 & 218 & - 55 & 0 & 0 & 1 & 0 & 0 \\ 119 & 83 & 7 & 82 & 106 & 0 & 0 & 0 & 1 & 0 \\ 162 & 20 & 175 & 143 & 74 & 0 & 0 & 0 & 0 & 1 \end{array}]$

Langkah 5.2

Perform the row operation $R_{2} = R_{2} - 20 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Langkah 5.2.1

Perform the row operation $R_{2} = R_{2} - 20 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 20 - 20 \cdot 1 & 169 - 20 (\frac{75}{44}) & - 164 - 20 (- \frac{15}{11}) & 18 - 20 (- \frac{3}{4}) & 105 - 20 (\frac{1}{4}) & 0 - 20 (\frac{1}{44}) & 1 - 20 \cdot 0 & 0 - 20 \cdot 0 & 0 - 20 \cdot 0 & 0 - 20 \cdot 0 \\ 113 & - 82 & 239 & 218 & - 55 & 0 & 0 & 1 & 0 & 0 \\ 119 & 83 & 7 & 82 & 106 & 0 & 0 & 0 & 1 & 0 \\ 162 & 20 & 175 & 143 & 74 & 0 & 0 & 0 & 0 & 1 \end{array}]$

Langkah 5.2.2

Sederhanakan $R_{2}$ .

Langkah 5.3

Perform the row operation $R_{3} = R_{3} - 113 R_{1}$ to make the entry at $3, 1$ a $0$ .

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Langkah 5.3.1

Perform the row operation $R_{3} = R_{3} - 113 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & \frac{1484}{11} & - \frac{1504}{11} & 33 & 100 & - \frac{5}{11} & 1 & 0 & 0 & 0 \\ 113 - 113 \cdot 1 & - 82 - 113 (\frac{75}{44}) & 239 - 113 (- \frac{15}{11}) & 218 - 113 (- \frac{3}{4}) & - 55 - 113 (\frac{1}{4}) & 0 - 113 (\frac{1}{44}) & 0 - 113 \cdot 0 & 1 - 113 \cdot 0 & 0 - 113 \cdot 0 & 0 - 113 \cdot 0 \\ 119 & 83 & 7 & 82 & 106 & 0 & 0 & 0 & 1 & 0 \\ 162 & 20 & 175 & 143 & 74 & 0 & 0 & 0 & 0 & 1 \end{array}]$

Langkah 5.3.2

Sederhanakan $R_{3}$ .

Langkah 5.4

Perform the row operation $R_{4} = R_{4} - 119 R_{1}$ to make the entry at $4, 1$ a $0$ .

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Langkah 5.4.1

Perform the row operation $R_{4} = R_{4} - 119 R_{1}$ to make the entry at $4, 1$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & \frac{1484}{11} & - \frac{1504}{11} & 33 & 100 & - \frac{5}{11} & 1 & 0 & 0 & 0 \\ 0 & - \frac{12083}{44} & \frac{4324}{11} & \frac{1211}{4} & - \frac{333}{4} & - \frac{113}{44} & 0 & 1 & 0 & 0 \\ 119 - 119 \cdot 1 & 83 - 119 (\frac{75}{44}) & 7 - 119 (- \frac{15}{11}) & 82 - 119 (- \frac{3}{4}) & 106 - 119 (\frac{1}{4}) & 0 - 119 (\frac{1}{44}) & 0 - 119 \cdot 0 & 0 - 119 \cdot 0 & 1 - 119 \cdot 0 & 0 - 119 \cdot 0 \\ 162 & 20 & 175 & 143 & 74 & 0 & 0 & 0 & 0 & 1 \end{array}]$

Langkah 5.4.2

Sederhanakan $R_{4}$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & \frac{1484}{11} & - \frac{1504}{11} & 33 & 100 & - \frac{5}{11} & 1 & 0 & 0 & 0 \\ 0 & - \frac{12083}{44} & \frac{4324}{11} & \frac{1211}{4} & - \frac{333}{4} & - \frac{113}{44} & 0 & 1 & 0 & 0 \\ 0 & - \frac{5273}{44} & \frac{1862}{11} & \frac{685}{4} & \frac{305}{4} & - \frac{119}{44} & 0 & 0 & 1 & 0 \\ 162 & 20 & 175 & 143 & 74 & 0 & 0 & 0 & 0 & 1 \end{array}]$

Langkah 5.5

Perform the row operation $R_{5} = R_{5} - 162 R_{1}$ to make the entry at $5, 1$ a $0$ .

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Langkah 5.5.1

Perform the row operation $R_{5} = R_{5} - 162 R_{1}$ to make the entry at $5, 1$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & \frac{1484}{11} & - \frac{1504}{11} & 33 & 100 & - \frac{5}{11} & 1 & 0 & 0 & 0 \\ 0 & - \frac{12083}{44} & \frac{4324}{11} & \frac{1211}{4} & - \frac{333}{4} & - \frac{113}{44} & 0 & 1 & 0 & 0 \\ 0 & - \frac{5273}{44} & \frac{1862}{11} & \frac{685}{4} & \frac{305}{4} & - \frac{119}{44} & 0 & 0 & 1 & 0 \\ 162 - 162 \cdot 1 & 20 - 162 (\frac{75}{44}) & 175 - 162 (- \frac{15}{11}) & 143 - 162 (- \frac{3}{4}) & 74 - 162 (\frac{1}{4}) & 0 - 162 (\frac{1}{44}) & 0 - 162 \cdot 0 & 0 - 162 \cdot 0 & 0 - 162 \cdot 0 & 1 - 162 \cdot 0 \end{array}]$

Langkah 5.5.2

Sederhanakan $R_{5}$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & \frac{1484}{11} & - \frac{1504}{11} & 33 & 100 & - \frac{5}{11} & 1 & 0 & 0 & 0 \\ 0 & - \frac{12083}{44} & \frac{4324}{11} & \frac{1211}{4} & - \frac{333}{4} & - \frac{113}{44} & 0 & 1 & 0 & 0 \\ 0 & - \frac{5273}{44} & \frac{1862}{11} & \frac{685}{4} & \frac{305}{4} & - \frac{119}{44} & 0 & 0 & 1 & 0 \\ 0 & - \frac{5635}{22} & \frac{4355}{11} & \frac{529}{2} & \frac{67}{2} & - \frac{81}{22} & 0 & 0 & 0 & 1 \end{array}]$

Langkah 5.6

Multiply each element of $R_{2}$ by $\frac{11}{1484}$ to make the entry at $2, 2$ a $1$ .

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Langkah 5.6.1

Multiply each element of $R_{2}$ by $\frac{11}{1484}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ \frac{11}{1484} \cdot 0 & \frac{11}{1484} \cdot \frac{1484}{11} & \frac{11}{1484} (- \frac{1504}{11}) & \frac{11}{1484} \cdot 33 & \frac{11}{1484} \cdot 100 & \frac{11}{1484} (- \frac{5}{11}) & \frac{11}{1484} \cdot 1 & \frac{11}{1484} \cdot 0 & \frac{11}{1484} \cdot 0 & \frac{11}{1484} \cdot 0 \\ 0 & - \frac{12083}{44} & \frac{4324}{11} & \frac{1211}{4} & - \frac{333}{4} & - \frac{113}{44} & 0 & 1 & 0 & 0 \\ 0 & - \frac{5273}{44} & \frac{1862}{11} & \frac{685}{4} & \frac{305}{4} & - \frac{119}{44} & 0 & 0 & 1 & 0 \\ 0 & - \frac{5635}{22} & \frac{4355}{11} & \frac{529}{2} & \frac{67}{2} & - \frac{81}{22} & 0 & 0 & 0 & 1 \end{array}]$

Langkah 5.6.2

Sederhanakan $R_{2}$ .

Langkah 5.7

Perform the row operation $R_{3} = R_{3} + \frac{12083}{44} R_{2}$ to make the entry at $3, 2$ a $0$ .

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Langkah 5.7.1

Perform the row operation $R_{3} = R_{3} + \frac{12083}{44} R_{2}$ to make the entry at $3, 2$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 + \frac{12083}{44} \cdot 0 & - \frac{12083}{44} + \frac{12083}{44} \cdot 1 & \frac{4324}{11} + \frac{12083}{44} (- \frac{376}{371}) & \frac{1211}{4} + \frac{12083}{44} \cdot \frac{363}{1484} & - \frac{333}{4} + \frac{12083}{44} \cdot \frac{275}{371} & - \frac{113}{44} + \frac{12083}{44} (- \frac{5}{1484}) & 0 + \frac{12083}{44} \cdot \frac{11}{1484} & 1 + \frac{12083}{44} \cdot 0 & 0 + \frac{12083}{44} \cdot 0 & 0 + \frac{12083}{44} \cdot 0 \\ 0 & - \frac{5273}{44} & \frac{1862}{11} & \frac{685}{4} & \frac{305}{4} & - \frac{119}{44} & 0 & 0 & 1 & 0 \\ 0 & - \frac{5635}{22} & \frac{4355}{11} & \frac{529}{2} & \frac{67}{2} & - \frac{81}{22} & 0 & 0 & 0 & 1 \end{array}]$

Langkah 5.7.2

Sederhanakan $R_{3}$ .

Langkah 5.8

Perform the row operation $R_{4} = R_{4} + \frac{5273}{44} R_{2}$ to make the entry at $4, 2$ a $0$ .

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Langkah 5.8.1

Perform the row operation $R_{4} = R_{4} + \frac{5273}{44} R_{2}$ to make the entry at $4, 2$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 & 0 & \frac{42582}{371} & \frac{2195863}{5936} & \frac{44633}{371} & - \frac{20737}{5936} & \frac{12083}{5936} & 1 & 0 & 0 \\ 0 + \frac{5273}{44} \cdot 0 & - \frac{5273}{44} + \frac{5273}{44} \cdot 1 & \frac{1862}{11} + \frac{5273}{44} (- \frac{376}{371}) & \frac{685}{4} + \frac{5273}{44} \cdot \frac{363}{1484} & \frac{305}{4} + \frac{5273}{44} \cdot \frac{275}{371} & - \frac{119}{44} + \frac{5273}{44} (- \frac{5}{1484}) & 0 + \frac{5273}{44} \cdot \frac{11}{1484} & 0 + \frac{5273}{44} \cdot 0 & 1 + \frac{5273}{44} \cdot 0 & 0 + \frac{5273}{44} \cdot 0 \\ 0 & - \frac{5635}{22} & \frac{4355}{11} & \frac{529}{2} & \frac{67}{2} & - \frac{81}{22} & 0 & 0 & 0 & 1 \end{array}]$

Langkah 5.8.2

Sederhanakan $R_{4}$ .

Langkah 5.9

Perform the row operation $R_{5} = R_{5} + \frac{5635}{22} R_{2}$ to make the entry at $5, 2$ a $0$ .

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Langkah 5.9.1

Perform the row operation $R_{5} = R_{5} + \frac{5635}{22} R_{2}$ to make the entry at $5, 2$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 & 0 & \frac{42582}{371} & \frac{2195863}{5936} & \frac{44633}{371} & - \frac{20737}{5936} & \frac{12083}{5936} & 1 & 0 & 0 \\ 0 & 0 & \frac{17740}{371} & \frac{1190549}{5936} & \frac{61245}{371} & - \frac{18451}{5936} & \frac{5273}{5936} & 0 & 1 & 0 \\ 0 + \frac{5635}{22} \cdot 0 & - \frac{5635}{22} + \frac{5635}{22} \cdot 1 & \frac{4355}{11} + \frac{5635}{22} (- \frac{376}{371}) & \frac{529}{2} + \frac{5635}{22} \cdot \frac{363}{1484} & \frac{67}{2} + \frac{5635}{22} \cdot \frac{275}{371} & - \frac{81}{22} + \frac{5635}{22} (- \frac{5}{1484}) & 0 + \frac{5635}{22} \cdot \frac{11}{1484} & 0 + \frac{5635}{22} \cdot 0 & 0 + \frac{5635}{22} \cdot 0 & 1 + \frac{5635}{22} \cdot 0 \end{array}]$

Langkah 5.9.2

Sederhanakan $R_{5}$ .

Langkah 5.10

Multiply each element of $R_{3}$ by $\frac{371}{42582}$ to make the entry at $3, 3$ a $1$ .

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Langkah 5.10.1

Multiply each element of $R_{3}$ by $\frac{371}{42582}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ \frac{371}{42582} \cdot 0 & \frac{371}{42582} \cdot 0 & \frac{371}{42582} \cdot \frac{42582}{371} & \frac{371}{42582} \cdot \frac{2195863}{5936} & \frac{371}{42582} \cdot \frac{44633}{371} & \frac{371}{42582} (- \frac{20737}{5936}) & \frac{371}{42582} \cdot \frac{12083}{5936} & \frac{371}{42582} \cdot 1 & \frac{371}{42582} \cdot 0 & \frac{371}{42582} \cdot 0 \\ 0 & 0 & \frac{17740}{371} & \frac{1190549}{5936} & \frac{61245}{371} & - \frac{18451}{5936} & \frac{5273}{5936} & 0 & 1 & 0 \\ 0 & 0 & \frac{7225}{53} & \frac{138713}{424} & \frac{11838}{53} & - \frac{1927}{424} & \frac{805}{424} & 0 & 0 & 1 \end{array}]$

Langkah 5.10.2

Sederhanakan $R_{3}$ .

Langkah 5.11

Perform the row operation $R_{4} = R_{4} - \frac{17740}{371} R_{3}$ to make the entry at $4, 3$ a $0$ .

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Langkah 5.11.1

Perform the row operation $R_{4} = R_{4} - \frac{17740}{371} R_{3}$ to make the entry at $4, 3$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{2195863}{681312} & \frac{44633}{42582} & - \frac{20737}{681312} & \frac{12083}{681312} & \frac{371}{42582} & 0 & 0 \\ 0 - \frac{17740}{371} \cdot 0 & 0 - \frac{17740}{371} \cdot 0 & \frac{17740}{371} - \frac{17740}{371} \cdot 1 & \frac{1190549}{5936} - \frac{17740}{371} \cdot \frac{2195863}{681312} & \frac{61245}{371} - \frac{17740}{371} \cdot \frac{44633}{42582} & - \frac{18451}{5936} - \frac{17740}{371} (- \frac{20737}{681312}) & \frac{5273}{5936} - \frac{17740}{371} \cdot \frac{12083}{681312} & 0 - \frac{17740}{371} \cdot \frac{371}{42582} & 1 - \frac{17740}{371} \cdot 0 & 0 - \frac{17740}{371} \cdot 0 \\ 0 & 0 & \frac{7225}{53} & \frac{138713}{424} & \frac{11838}{53} & - \frac{1927}{424} & \frac{805}{424} & 0 & 0 & 1 \end{array}]$

Langkah 5.11.2

Sederhanakan $R_{4}$ .

Langkah 5.12

Perform the row operation $R_{5} = R_{5} - \frac{7225}{53} R_{3}$ to make the entry at $5, 3$ a $0$ .

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Langkah 5.12.1

Perform the row operation $R_{5} = R_{5} - \frac{7225}{53} R_{3}$ to make the entry at $5, 3$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{2195863}{681312} & \frac{44633}{42582} & - \frac{20737}{681312} & \frac{12083}{681312} & \frac{371}{42582} & 0 & 0 \\ 0 & 0 & 0 & \frac{15823919}{340656} & \frac{2447635}{21291} & - \frac{563081}{340656} & \frac{13723}{340656} & - \frac{8870}{21291} & 1 & 0 \\ 0 - \frac{7225}{53} \cdot 0 & 0 - \frac{7225}{53} \cdot 0 & \frac{7225}{53} - \frac{7225}{53} \cdot 1 & \frac{138713}{424} - \frac{7225}{53} \cdot \frac{2195863}{681312} & \frac{11838}{53} - \frac{7225}{53} \cdot \frac{44633}{42582} & - \frac{1927}{424} - \frac{7225}{53} (- \frac{20737}{681312}) & \frac{805}{424} - \frac{7225}{53} \cdot \frac{12083}{681312} & 0 - \frac{7225}{53} \cdot \frac{371}{42582} & 0 - \frac{7225}{53} \cdot 0 & 1 - \frac{7225}{53} \cdot 0 \end{array}]$

Langkah 5.12.2

Sederhanakan $R_{5}$ .

Langkah 5.13

Multiply each element of $R_{4}$ by $\frac{340656}{15823919}$ to make the entry at $4, 4$ a $1$ .

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Langkah 5.13.1

Multiply each element of $R_{4}$ by $\frac{340656}{15823919}$ to make the entry at $4, 4$ a $1$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{2195863}{681312} & \frac{44633}{42582} & - \frac{20737}{681312} & \frac{12083}{681312} & \frac{371}{42582} & 0 & 0 \\ \frac{340656}{15823919} \cdot 0 & \frac{340656}{15823919} \cdot 0 & \frac{340656}{15823919} \cdot 0 & \frac{340656}{15823919} \cdot \frac{15823919}{340656} & \frac{340656}{15823919} \cdot \frac{2447635}{21291} & \frac{340656}{15823919} (- \frac{563081}{340656}) & \frac{340656}{15823919} \cdot \frac{13723}{340656} & \frac{340656}{15823919} (- \frac{8870}{21291}) & \frac{340656}{15823919} \cdot 1 & \frac{340656}{15823919} \cdot 0 \\ 0 & 0 & 0 & - \frac{76448231}{681312} & \frac{3426647}{42582} & - \frac{269551}{681312} & - \frac{353635}{681312} & - \frac{50575}{42582} & 0 & 1 \end{array}]$

Langkah 5.13.2

Sederhanakan $R_{4}$ .

Langkah 5.14

Perform the row operation $R_{5} = R_{5} + \frac{76448231}{681312} R_{4}$ to make the entry at $5, 4$ a $0$ .

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Langkah 5.14.1

Perform the row operation $R_{5} = R_{5} + \frac{76448231}{681312} R_{4}$ to make the entry at $5, 4$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{2195863}{681312} & \frac{44633}{42582} & - \frac{20737}{681312} & \frac{12083}{681312} & \frac{371}{42582} & 0 & 0 \\ 0 & 0 & 0 & 1 & \frac{39162160}{15823919} & - \frac{563081}{15823919} & \frac{13723}{15823919} & - \frac{141920}{15823919} & \frac{340656}{15823919} & 0 \\ 0 + \frac{76448231}{681312} \cdot 0 & 0 + \frac{76448231}{681312} \cdot 0 & 0 + \frac{76448231}{681312} \cdot 0 & - \frac{76448231}{681312} + \frac{76448231}{681312} \cdot 1 & \frac{3426647}{42582} + \frac{76448231}{681312} \cdot \frac{39162160}{15823919} & - \frac{269551}{681312} + \frac{76448231}{681312} (- \frac{563081}{15823919}) & - \frac{353635}{681312} + \frac{76448231}{681312} \cdot \frac{13723}{15823919} & - \frac{50575}{42582} + \frac{76448231}{681312} (- \frac{141920}{15823919}) & 0 + \frac{76448231}{681312} \cdot \frac{340656}{15823919} & 1 + \frac{76448231}{681312} \cdot 0 \end{array}]$

Langkah 5.14.2

Sederhanakan $R_{5}$ .

Langkah 5.15

Multiply each element of $R_{5}$ by $\frac{15823919}{5667661229}$ to make the entry at $5, 5$ a $1$ .

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Langkah 5.15.1

Multiply each element of $R_{5}$ by $\frac{15823919}{5667661229}$ to make the entry at $5, 5$ a $1$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{2195863}{681312} & \frac{44633}{42582} & - \frac{20737}{681312} & \frac{12083}{681312} & \frac{371}{42582} & 0 & 0 \\ 0 & 0 & 0 & 1 & \frac{39162160}{15823919} & - \frac{563081}{15823919} & \frac{13723}{15823919} & - \frac{141920}{15823919} & \frac{340656}{15823919} & 0 \\ \frac{15823919}{5667661229} \cdot 0 & \frac{15823919}{5667661229} \cdot 0 & \frac{15823919}{5667661229} \cdot 0 & \frac{15823919}{5667661229} \cdot 0 & \frac{15823919}{5667661229} \cdot \frac{5667661229}{15823919} & \frac{15823919}{5667661229} (- \frac{69442340}{15823919}) & \frac{15823919}{5667661229} (- \frac{13347167}{31647838}) & \frac{15823919}{5667661229} (- \frac{69437345}{31647838}) & \frac{15823919}{5667661229} \cdot \frac{76448231}{31647838} & \frac{15823919}{5667661229} \cdot 1 \end{array}]$

Langkah 5.15.2

Sederhanakan $R_{5}$ .

Langkah 5.16

Perform the row operation $R_{4} = R_{4} - \frac{39162160}{15823919} R_{5}$ to make the entry at $4, 5$ a $0$ .

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Langkah 5.16.1

Perform the row operation $R_{4} = R_{4} - \frac{39162160}{15823919} R_{5}$ to make the entry at $4, 5$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{2195863}{681312} & \frac{44633}{42582} & - \frac{20737}{681312} & \frac{12083}{681312} & \frac{371}{42582} & 0 & 0 \\ 0 - \frac{39162160}{15823919} \cdot 0 & 0 - \frac{39162160}{15823919} \cdot 0 & 0 - \frac{39162160}{15823919} \cdot 0 & 1 - \frac{39162160}{15823919} \cdot 0 & \frac{39162160}{15823919} - \frac{39162160}{15823919} \cdot 1 & - \frac{563081}{15823919} - \frac{39162160}{15823919} (- \frac{69442340}{5667661229}) & \frac{13723}{15823919} - \frac{39162160}{15823919} (- \frac{13347167}{11335322458}) & - \frac{141920}{15823919} - \frac{39162160}{15823919} (- \frac{69437345}{11335322458}) & \frac{340656}{15823919} - \frac{39162160}{15823919} \cdot \frac{76448231}{11335322458} & 0 - \frac{39162160}{15823919} \cdot \frac{15823919}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Langkah 5.16.2

Sederhanakan $R_{4}$ .

Langkah 5.17

Perform the row operation $R_{3} = R_{3} - \frac{44633}{42582} R_{5}$ to make the entry at $3, 5$ a $0$ .

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Langkah 5.17.1

Perform the row operation $R_{3} = R_{3} - \frac{44633}{42582} R_{5}$ to make the entry at $3, 5$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 - \frac{44633}{42582} \cdot 0 & 0 - \frac{44633}{42582} \cdot 0 & 1 - \frac{44633}{42582} \cdot 0 & \frac{2195863}{681312} - \frac{44633}{42582} \cdot 0 & \frac{44633}{42582} - \frac{44633}{42582} \cdot 1 & - \frac{20737}{681312} - \frac{44633}{42582} (- \frac{69442340}{5667661229}) & \frac{12083}{681312} - \frac{44633}{42582} (- \frac{13347167}{11335322458}) & \frac{371}{42582} - \frac{44633}{42582} (- \frac{69437345}{11335322458}) & 0 - \frac{44633}{42582} \cdot \frac{76448231}{11335322458} & 0 - \frac{44633}{42582} \cdot \frac{15823919}{5667661229} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Langkah 5.17.2

Sederhanakan $R_{3}$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{2195863}{681312} & 0 & - \frac{67939571526253}{3861445607252448} & \frac{24416047822565}{1287148535750816} & \frac{2434867217101}{160893566968852} & - \frac{3412113894223}{482680700906556} & - \frac{706268976727}{241340350453278} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Langkah 5.18

Perform the row operation $R_{2} = R_{2} - \frac{275}{371} R_{5}$ to make the entry at $2, 5$ a $0$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.18.1

Perform the row operation $R_{2} = R_{2} - \frac{275}{371} R_{5}$ to make the entry at $2, 5$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 - \frac{275}{371} \cdot 0 & 1 - \frac{275}{371} \cdot 0 & - \frac{376}{371} - \frac{275}{371} \cdot 0 & \frac{363}{1484} - \frac{275}{371} \cdot 0 & \frac{275}{371} - \frac{275}{371} \cdot 1 & - \frac{5}{1484} - \frac{275}{371} (- \frac{69442340}{5667661229}) & \frac{11}{1484} - \frac{275}{371} (- \frac{13347167}{11335322458}) & 0 - \frac{275}{371} (- \frac{69437345}{11335322458}) & 0 - \frac{275}{371} \cdot \frac{76448231}{11335322458} & 0 - \frac{275}{371} \cdot \frac{15823919}{5667661229} \\ 0 & 0 & 1 & \frac{2195863}{681312} & 0 & - \frac{67939571526253}{3861445607252448} & \frac{24416047822565}{1287148535750816} & \frac{2434867217101}{160893566968852} & - \frac{3412113894223}{482680700906556} & - \frac{706268976727}{241340350453278} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Langkah 5.18.2

Sederhanakan $R_{2}$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & 0 & \frac{6864038265}{1201544180548} & \frac{9955030767}{1201544180548} & \frac{19095269875}{4205404631918} & - \frac{21023263525}{4205404631918} & - \frac{4351577725}{2102702315959} \\ 0 & 0 & 1 & \frac{2195863}{681312} & 0 & - \frac{67939571526253}{3861445607252448} & \frac{24416047822565}{1287148535750816} & \frac{2434867217101}{160893566968852} & - \frac{3412113894223}{482680700906556} & - \frac{706268976727}{241340350453278} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Langkah 5.19

Perform the row operation $R_{1} = R_{1} - \frac{1}{4} R_{5}$ to make the entry at $1, 5$ a $0$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.19.1

Perform the row operation $R_{1} = R_{1} - \frac{1}{4} R_{5}$ to make the entry at $1, 5$ a $0$ .

$[\begin{array}{c} 1 - \frac{1}{4} \cdot 0 & \frac{75}{44} - \frac{1}{4} \cdot 0 & - \frac{15}{11} - \frac{1}{4} \cdot 0 & - \frac{3}{4} - \frac{1}{4} \cdot 0 & \frac{1}{4} - \frac{1}{4} \cdot 1 & \frac{1}{44} - \frac{1}{4} (- \frac{69442340}{5667661229}) & 0 - \frac{1}{4} (- \frac{13347167}{11335322458}) & 0 - \frac{1}{4} (- \frac{69437345}{11335322458}) & 0 - \frac{1}{4} \cdot \frac{76448231}{11335322458} & 0 - \frac{1}{4} \cdot \frac{15823919}{5667661229} \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & 0 & \frac{6864038265}{1201544180548} & \frac{9955030767}{1201544180548} & \frac{19095269875}{4205404631918} & - \frac{21023263525}{4205404631918} & - \frac{4351577725}{2102702315959} \\ 0 & 0 & 1 & \frac{2195863}{681312} & 0 & - \frac{67939571526253}{3861445607252448} & \frac{24416047822565}{1287148535750816} & \frac{2434867217101}{160893566968852} & - \frac{3412113894223}{482680700906556} & - \frac{706268976727}{241340350453278} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Langkah 5.19.2

Sederhanakan $R_{1}$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & 0 & \frac{6431526969}{249377094076} & \frac{13347167}{45341289832} & \frac{69437345}{45341289832} & - \frac{76448231}{45341289832} & - \frac{15823919}{22670644916} \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & 0 & \frac{6864038265}{1201544180548} & \frac{9955030767}{1201544180548} & \frac{19095269875}{4205404631918} & - \frac{21023263525}{4205404631918} & - \frac{4351577725}{2102702315959} \\ 0 & 0 & 1 & \frac{2195863}{681312} & 0 & - \frac{67939571526253}{3861445607252448} & \frac{24416047822565}{1287148535750816} & \frac{2434867217101}{160893566968852} & - \frac{3412113894223}{482680700906556} & - \frac{706268976727}{241340350453278} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Langkah 5.20

Perform the row operation $R_{3} = R_{3} - \frac{2195863}{681312} R_{4}$ to make the entry at $3, 4$ a $0$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.20.1

Perform the row operation $R_{3} = R_{3} - \frac{2195863}{681312} R_{4}$ to make the entry at $3, 4$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & 0 & \frac{6431526969}{249377094076} & \frac{13347167}{45341289832} & \frac{69437345}{45341289832} & - \frac{76448231}{45341289832} & - \frac{15823919}{22670644916} \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & 0 & \frac{6864038265}{1201544180548} & \frac{9955030767}{1201544180548} & \frac{19095269875}{4205404631918} & - \frac{21023263525}{4205404631918} & - \frac{4351577725}{2102702315959} \\ 0 - \frac{2195863}{681312} \cdot 0 & 0 - \frac{2195863}{681312} \cdot 0 & 1 - \frac{2195863}{681312} \cdot 0 & \frac{2195863}{681312} - \frac{2195863}{681312} \cdot 1 & 0 - \frac{2195863}{681312} \cdot 0 & - \frac{67939571526253}{3861445607252448} - \frac{2195863}{681312} (- \frac{29818171}{5667661229}) & \frac{24416047822565}{1287148535750816} - \frac{2195863}{681312} \cdot \frac{21431433}{5667661229} & \frac{2434867217101}{160893566968852} - \frac{2195863}{681312} \cdot \frac{35092680}{5667661229} & - \frac{3412113894223}{482680700906556} - \frac{2195863}{681312} \cdot \frac{27413176}{5667661229} & - \frac{706268976727}{241340350453278} - \frac{2195863}{681312} (- \frac{39162160}{5667661229}) \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Langkah 5.20.2

Sederhanakan $R_{3}$ .

Langkah 5.21

Perform the row operation $R_{2} = R_{2} - \frac{363}{1484} R_{4}$ to make the entry at $2, 4$ a $0$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.21.1

Perform the row operation $R_{2} = R_{2} - \frac{363}{1484} R_{4}$ to make the entry at $2, 4$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & 0 & \frac{6431526969}{249377094076} & \frac{13347167}{45341289832} & \frac{69437345}{45341289832} & - \frac{76448231}{45341289832} & - \frac{15823919}{22670644916} \\ 0 - \frac{363}{1484} \cdot 0 & 1 - \frac{363}{1484} \cdot 0 & - \frac{376}{371} - \frac{363}{1484} \cdot 0 & \frac{363}{1484} - \frac{363}{1484} \cdot 1 & 0 - \frac{363}{1484} \cdot 0 & \frac{6864038265}{1201544180548} - \frac{363}{1484} (- \frac{29818171}{5667661229}) & \frac{9955030767}{1201544180548} - \frac{363}{1484} \cdot \frac{21431433}{5667661229} & \frac{19095269875}{4205404631918} - \frac{363}{1484} \cdot \frac{35092680}{5667661229} & - \frac{21023263525}{4205404631918} - \frac{363}{1484} \cdot \frac{27413176}{5667661229} & - \frac{4351577725}{2102702315959} - \frac{363}{1484} (- \frac{39162160}{5667661229}) \\ 0 & 0 & 1 & 0 & 0 & - \frac{3615015}{5667661229} & \frac{38437093}{5667661229} & - \frac{27332418}{5667661229} & - \frac{128417656}{5667661229} & \frac{109633229}{5667661229} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Langkah 5.21.2

Sederhanakan $R_{2}$ .

Langkah 5.22

Perform the row operation $R_{1} = R_{1} + \frac{3}{4} R_{4}$ to make the entry at $1, 4$ a $0$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.22.1

Perform the row operation $R_{1} = R_{1} + \frac{3}{4} R_{4}$ to make the entry at $1, 4$ a $0$ .

$[\begin{array}{c} 1 + \frac{3}{4} \cdot 0 & \frac{75}{44} + \frac{3}{4} \cdot 0 & - \frac{15}{11} + \frac{3}{4} \cdot 0 & - \frac{3}{4} + \frac{3}{4} \cdot 1 & 0 + \frac{3}{4} \cdot 0 & \frac{6431526969}{249377094076} + \frac{3}{4} (- \frac{29818171}{5667661229}) & \frac{13347167}{45341289832} + \frac{3}{4} \cdot \frac{21431433}{5667661229} & \frac{69437345}{45341289832} + \frac{3}{4} \cdot \frac{35092680}{5667661229} & - \frac{76448231}{45341289832} + \frac{3}{4} \cdot \frac{27413176}{5667661229} & - \frac{15823919}{22670644916} + \frac{3}{4} (- \frac{39162160}{5667661229}) \\ 0 & 1 & - \frac{376}{371} & 0 & 0 & \frac{14718065982}{2102702315959} & \frac{30952802595}{4205404631918} & \frac{240112235}{79347257206} & - \frac{25998754969}{4205404631918} & - \frac{797611705}{2102702315959} \\ 0 & 0 & 1 & 0 & 0 & - \frac{3615015}{5667661229} & \frac{38437093}{5667661229} & - \frac{27332418}{5667661229} & - \frac{128417656}{5667661229} & \frac{109633229}{5667661229} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Langkah 5.22.2

Sederhanakan $R_{1}$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & 0 & 0 & \frac{1892817}{86649442} & \frac{98635}{31508888} & \frac{194575}{31508888} & \frac{61175}{31508888} & - \frac{92641}{15754444} \\ 0 & 1 & - \frac{376}{371} & 0 & 0 & \frac{14718065982}{2102702315959} & \frac{30952802595}{4205404631918} & \frac{240112235}{79347257206} & - \frac{25998754969}{4205404631918} & - \frac{797611705}{2102702315959} \\ 0 & 0 & 1 & 0 & 0 & - \frac{3615015}{5667661229} & \frac{38437093}{5667661229} & - \frac{27332418}{5667661229} & - \frac{128417656}{5667661229} & \frac{109633229}{5667661229} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Langkah 5.23

Perform the row operation $R_{2} = R_{2} + \frac{376}{371} R_{3}$ to make the entry at $2, 3$ a $0$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.23.1

Perform the row operation $R_{2} = R_{2} + \frac{376}{371} R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & 0 & 0 & \frac{1892817}{86649442} & \frac{98635}{31508888} & \frac{194575}{31508888} & \frac{61175}{31508888} & - \frac{92641}{15754444} \\ 0 + \frac{376}{371} \cdot 0 & 1 + \frac{376}{371} \cdot 0 & - \frac{376}{371} + \frac{376}{371} \cdot 1 & 0 + \frac{376}{371} \cdot 0 & 0 + \frac{376}{371} \cdot 0 & \frac{14718065982}{2102702315959} + \frac{376}{371} (- \frac{3615015}{5667661229}) & \frac{30952802595}{4205404631918} + \frac{376}{371} \cdot \frac{38437093}{5667661229} & \frac{240112235}{79347257206} + \frac{376}{371} (- \frac{27332418}{5667661229}) & - \frac{25998754969}{4205404631918} + \frac{376}{371} (- \frac{128417656}{5667661229}) & - \frac{797611705}{2102702315959} + \frac{376}{371} \cdot \frac{109633229}{5667661229} \\ 0 & 0 & 1 & 0 & 0 & - \frac{3615015}{5667661229} & \frac{38437093}{5667661229} & - \frac{27332418}{5667661229} & - \frac{128417656}{5667661229} & \frac{109633229}{5667661229} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Langkah 5.23.2

Sederhanakan $R_{2}$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & 0 & 0 & \frac{1892817}{86649442} & \frac{98635}{31508888} & \frac{194575}{31508888} & \frac{61175}{31508888} & - \frac{92641}{15754444} \\ 0 & 1 & 0 & 0 & 0 & \frac{36007602}{5667661229} & \frac{161340961}{11335322458} & - \frac{21099811}{11335322458} & - \frac{330374211}{11335322458} & \frac{108960869}{5667661229} \\ 0 & 0 & 1 & 0 & 0 & - \frac{3615015}{5667661229} & \frac{38437093}{5667661229} & - \frac{27332418}{5667661229} & - \frac{128417656}{5667661229} & \frac{109633229}{5667661229} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Langkah 5.24

Perform the row operation $R_{1} = R_{1} + \frac{15}{11} R_{3}$ to make the entry at $1, 3$ a $0$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.24.1

Perform the row operation $R_{1} = R_{1} + \frac{15}{11} R_{3}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 + \frac{15}{11} \cdot 0 & \frac{75}{44} + \frac{15}{11} \cdot 0 & - \frac{15}{11} + \frac{15}{11} \cdot 1 & 0 + \frac{15}{11} \cdot 0 & 0 + \frac{15}{11} \cdot 0 & \frac{1892817}{86649442} + \frac{15}{11} (- \frac{3615015}{5667661229}) & \frac{98635}{31508888} + \frac{15}{11} \cdot \frac{38437093}{5667661229} & \frac{194575}{31508888} + \frac{15}{11} (- \frac{27332418}{5667661229}) & \frac{61175}{31508888} + \frac{15}{11} (- \frac{128417656}{5667661229}) & - \frac{92641}{15754444} + \frac{15}{11} \cdot \frac{109633229}{5667661229} \\ 0 & 1 & 0 & 0 & 0 & \frac{36007602}{5667661229} & \frac{161340961}{11335322458} & - \frac{21099811}{11335322458} & - \frac{330374211}{11335322458} & \frac{108960869}{5667661229} \\ 0 & 0 & 1 & 0 & 0 & - \frac{3615015}{5667661229} & \frac{38437093}{5667661229} & - \frac{27332418}{5667661229} & - \frac{128417656}{5667661229} & \frac{109633229}{5667661229} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Langkah 5.24.2

Sederhanakan $R_{1}$ .

$[\begin{array}{c} 1 & \frac{75}{44} & 0 & 0 & 0 & \frac{2615313213}{124688547038} & \frac{6173744575}{498754188152} & - \frac{199962485}{498754188152} & - \frac{14441779645}{498754188152} & \frac{5111579351}{249377094076} \\ 0 & 1 & 0 & 0 & 0 & \frac{36007602}{5667661229} & \frac{161340961}{11335322458} & - \frac{21099811}{11335322458} & - \frac{330374211}{11335322458} & \frac{108960869}{5667661229} \\ 0 & 0 & 1 & 0 & 0 & - \frac{3615015}{5667661229} & \frac{38437093}{5667661229} & - \frac{27332418}{5667661229} & - \frac{128417656}{5667661229} & \frac{109633229}{5667661229} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Langkah 5.25

Perform the row operation $R_{1} = R_{1} - \frac{75}{44} R_{2}$ to make the entry at $1, 2$ a $0$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.25.1

Perform the row operation $R_{1} = R_{1} - \frac{75}{44} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - \frac{75}{44} \cdot 0 & \frac{75}{44} - \frac{75}{44} \cdot 1 & 0 - \frac{75}{44} \cdot 0 & 0 - \frac{75}{44} \cdot 0 & 0 - \frac{75}{44} \cdot 0 & \frac{2615313213}{124688547038} - \frac{75}{44} \cdot \frac{36007602}{5667661229} & \frac{6173744575}{498754188152} - \frac{75}{44} \cdot \frac{161340961}{11335322458} & - \frac{199962485}{498754188152} - \frac{75}{44} (- \frac{21099811}{11335322458}) & - \frac{14441779645}{498754188152} - \frac{75}{44} (- \frac{330374211}{11335322458}) & \frac{5111579351}{249377094076} - \frac{75}{44} \cdot \frac{108960869}{5667661229} \\ 0 & 1 & 0 & 0 & 0 & \frac{36007602}{5667661229} & \frac{161340961}{11335322458} & - \frac{21099811}{11335322458} & - \frac{330374211}{11335322458} & \frac{108960869}{5667661229} \\ 0 & 0 & 1 & 0 & 0 & - \frac{3615015}{5667661229} & \frac{38437093}{5667661229} & - \frac{27332418}{5667661229} & - \frac{128417656}{5667661229} & \frac{109633229}{5667661229} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Langkah 5.25.2

Sederhanakan $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 0 & 0 & 0 & \frac{57501279}{5667661229} & - \frac{134700625}{11335322458} & \frac{31420985}{11335322458} & \frac{234915595}{11335322458} & - \frac{69556496}{5667661229} \\ 0 & 1 & 0 & 0 & 0 & \frac{36007602}{5667661229} & \frac{161340961}{11335322458} & - \frac{21099811}{11335322458} & - \frac{330374211}{11335322458} & \frac{108960869}{5667661229} \\ 0 & 0 & 1 & 0 & 0 & - \frac{3615015}{5667661229} & \frac{38437093}{5667661229} & - \frac{27332418}{5667661229} & - \frac{128417656}{5667661229} & \frac{109633229}{5667661229} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Langkah 6

The right half of the reduced row echelon form is the inverse.

$[\begin{array}{c} \frac{57501279}{5667661229} & - \frac{134700625}{11335322458} & \frac{31420985}{11335322458} & \frac{234915595}{11335322458} & - \frac{69556496}{5667661229} \\ \frac{36007602}{5667661229} & \frac{161340961}{11335322458} & - \frac{21099811}{11335322458} & - \frac{330374211}{11335322458} & \frac{108960869}{5667661229} \\ - \frac{3615015}{5667661229} & \frac{38437093}{5667661229} & - \frac{27332418}{5667661229} & - \frac{128417656}{5667661229} & \frac{109633229}{5667661229} \\ - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$