Aljabar Linear Contoh

$[\begin{array}{c} 1 & - 2 & 3 & - 5 & 7 \\ 2 & 0 & - 1 & - 5 & 6 \\ 4 & 7 & 3 & - 9 & 4 \\ 3 & 1 & - 2 & - 2 & 3 \\ - 5 & - 1 & 3 & 7 & - 9 \end{array}]$

Langkah 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 $2$ by its cofactor and add.

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Langkah 1.1

Consider the corresponding sign chart.

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

Langkah 1.2

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

Langkah 1.3

The minor for $a_{21}$ is the determinant with row $2$ and column $1$ deleted.

$| \begin{array}{c} - 2 & 3 & - 5 & 7 \\ 7 & 3 & - 9 & 4 \\ 1 & - 2 & - 2 & 3 \\ - 1 & 3 & 7 & - 9 \end{array} |$

Langkah 1.4

Multiply element $a_{21}$ by its cofactor.

$- 2 | \begin{array}{c} - 2 & 3 & - 5 & 7 \\ 7 & 3 & - 9 & 4 \\ 1 & - 2 & - 2 & 3 \\ - 1 & 3 & 7 & - 9 \end{array} |$

Langkah 1.5

The minor for $a_{22}$ is the determinant with row $2$ and column $2$ deleted.

$| \begin{array}{c} 1 & 3 & - 5 & 7 \\ 4 & 3 & - 9 & 4 \\ 3 & - 2 & - 2 & 3 \\ - 5 & 3 & 7 & - 9 \end{array} |$

Langkah 1.6

Multiply element $a_{22}$ by its cofactor.

$0 | \begin{array}{c} 1 & 3 & - 5 & 7 \\ 4 & 3 & - 9 & 4 \\ 3 & - 2 & - 2 & 3 \\ - 5 & 3 & 7 & - 9 \end{array} |$

Langkah 1.7

The minor for $a_{23}$ is the determinant with row $2$ and column $3$ deleted.

$| \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} |$

Langkah 1.8

Multiply element $a_{23}$ by its cofactor.

$1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} |$

Langkah 1.9

The minor for $a_{24}$ is the determinant with row $2$ and column $4$ deleted.

$| \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} |$

Langkah 1.10

Multiply element $a_{24}$ by its cofactor.

$- 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} |$

Langkah 1.11

The minor for $a_{25}$ is the determinant with row $2$ and column $5$ deleted.

$| \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 1.12

Multiply element $a_{25}$ by its cofactor.

$- 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 1.13

Add the terms together.

$- 2 | \begin{array}{c} - 2 & 3 & - 5 & 7 \\ 7 & 3 & - 9 & 4 \\ 1 & - 2 & - 2 & 3 \\ - 1 & 3 & 7 & - 9 \end{array} | + 0 | \begin{array}{c} 1 & 3 & - 5 & 7 \\ 4 & 3 & - 9 & 4 \\ 3 & - 2 & - 2 & 3 \\ - 5 & 3 & 7 & - 9 \end{array} | + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 2

Kalikan $0$ dengan $| \begin{array}{c} 1 & 3 & - 5 & 7 \\ 4 & 3 & - 9 & 4 \\ 3 & - 2 & - 2 & 3 \\ - 5 & 3 & 7 & - 9 \end{array} |$ .

$- 2 | \begin{array}{c} - 2 & 3 & - 5 & 7 \\ 7 & 3 & - 9 & 4 \\ 1 & - 2 & - 2 & 3 \\ - 1 & 3 & 7 & - 9 \end{array} | + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3

Evaluasi $| \begin{array}{c} - 2 & 3 & - 5 & 7 \\ 7 & 3 & - 9 & 4 \\ 1 & - 2 & - 2 & 3 \\ - 1 & 3 & 7 & - 9 \end{array} |$ .

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Langkah 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 3.1.1

Consider the corresponding sign chart.

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

Langkah 3.1.2

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

Langkah 3.1.3

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

$| \begin{array}{c} 3 & - 9 & 4 \\ - 2 & - 2 & 3 \\ 3 & 7 & - 9 \end{array} |$

Langkah 3.1.4

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

$- 2 | \begin{array}{c} 3 & - 9 & 4 \\ - 2 & - 2 & 3 \\ 3 & 7 & - 9 \end{array} |$

Langkah 3.1.5

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

$| \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} |$

Langkah 3.1.6

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

$- 3 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} |$

Langkah 3.1.7

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

$| \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} |$

Langkah 3.1.8

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

$- 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} |$

Langkah 3.1.9

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

$| \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |$

Langkah 3.1.10

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

$- 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |$

Langkah 3.1.11

Add the terms together.

$- 2 (- 2 | \begin{array}{c} 3 & - 9 & 4 \\ - 2 & - 2 & 3 \\ 3 & 7 & - 9 \end{array} | - 3 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.2

Evaluasi $| \begin{array}{c} 3 & - 9 & 4 \\ - 2 & - 2 & 3 \\ 3 & 7 & - 9 \end{array} |$ .

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Langkah 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 3.2.1.1

Consider the corresponding sign chart.

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

Langkah 3.2.1.2

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

Langkah 3.2.1.3

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

$| \begin{array}{c} - 2 & 3 \\ 7 & - 9 \end{array} |$

Langkah 3.2.1.4

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

$3 | \begin{array}{c} - 2 & 3 \\ 7 & - 9 \end{array} |$

Langkah 3.2.1.5

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

$| \begin{array}{c} - 2 & 3 \\ 3 & - 9 \end{array} |$

Langkah 3.2.1.6

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

$9 | \begin{array}{c} - 2 & 3 \\ 3 & - 9 \end{array} |$

Langkah 3.2.1.7

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

$| \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |$

Langkah 3.2.1.8

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

$4 | \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |$

Langkah 3.2.1.9

Add the terms together.

$- 2 (- 2 (3 | \begin{array}{c} - 2 & 3 \\ 7 & - 9 \end{array} | + 9 | \begin{array}{c} - 2 & 3 \\ 3 & - 9 \end{array} | + 4 | \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |) - 3 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.2.2

Evaluasi $| \begin{array}{c} - 2 & 3 \\ 7 & - 9 \end{array} |$ .

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Langkah 3.2.2.1

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

$- 2 (- 2 (3 (- 2 \cdot - 9 - 7 \cdot 3) + 9 | \begin{array}{c} - 2 & 3 \\ 3 & - 9 \end{array} | + 4 | \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |) - 3 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.2.2.2

Sederhanakan determinannya.

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Langkah 3.2.2.2.1

Sederhanakan setiap suku.

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Langkah 3.2.2.2.1.1

Kalikan $- 2$ dengan $- 9$ .

$- 2 (- 2 (3 (18 - 7 \cdot 3) + 9 | \begin{array}{c} - 2 & 3 \\ 3 & - 9 \end{array} | + 4 | \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |) - 3 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.2.2.2.1.2

Kalikan $- 7$ dengan $3$ .

$- 2 (- 2 (3 (18 - 21) + 9 | \begin{array}{c} - 2 & 3 \\ 3 & - 9 \end{array} | + 4 | \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |) - 3 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.2.2.2.2

Kurangi $21$ dengan $18$ .

$- 2 (- 2 (3 \cdot - 3 + 9 | \begin{array}{c} - 2 & 3 \\ 3 & - 9 \end{array} | + 4 | \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |) - 3 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.2.3

Evaluasi $| \begin{array}{c} - 2 & 3 \\ 3 & - 9 \end{array} |$ .

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Langkah 3.2.3.1

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

$- 2 (- 2 (3 \cdot - 3 + 9 (- 2 \cdot - 9 - 3 \cdot 3) + 4 | \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |) - 3 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.2.3.2

Sederhanakan determinannya.

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Langkah 3.2.3.2.1

Sederhanakan setiap suku.

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Langkah 3.2.3.2.1.1

Kalikan $- 2$ dengan $- 9$ .

$- 2 (- 2 (3 \cdot - 3 + 9 (18 - 3 \cdot 3) + 4 | \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |) - 3 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.2.3.2.1.2

Kalikan $- 3$ dengan $3$ .

$- 2 (- 2 (3 \cdot - 3 + 9 (18 - 9) + 4 | \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |) - 3 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.2.3.2.2

Kurangi $9$ dengan $18$ .

$- 2 (- 2 (3 \cdot - 3 + 9 \cdot 9 + 4 | \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |) - 3 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.2.4

Evaluasi $| \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |$ .

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Langkah 3.2.4.1

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

$- 2 (- 2 (3 \cdot - 3 + 9 \cdot 9 + 4 (- 2 \cdot 7 - 3 \cdot - 2)) - 3 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.2.4.2

Sederhanakan determinannya.

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Langkah 3.2.4.2.1

Sederhanakan setiap suku.

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Langkah 3.2.4.2.1.1

Kalikan $- 2$ dengan $7$ .

$- 2 (- 2 (3 \cdot - 3 + 9 \cdot 9 + 4 (- 14 - 3 \cdot - 2)) - 3 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.2.4.2.1.2

Kalikan $- 3$ dengan $- 2$ .

$- 2 (- 2 (3 \cdot - 3 + 9 \cdot 9 + 4 (- 14 + 6)) - 3 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.2.4.2.2

Tambahkan $- 14$ dan $6$ .

$- 2 (- 2 (3 \cdot - 3 + 9 \cdot 9 + 4 \cdot - 8) - 3 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.2.5

Sederhanakan determinannya.

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Langkah 3.2.5.1

Sederhanakan setiap suku.

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Langkah 3.2.5.1.1

Kalikan $3$ dengan $- 3$ .

$- 2 (- 2 (- 9 + 9 \cdot 9 + 4 \cdot - 8) - 3 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.2.5.1.2

Kalikan $9$ dengan $9$ .

$- 2 (- 2 (- 9 + 81 + 4 \cdot - 8) - 3 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.2.5.1.3

Kalikan $4$ dengan $- 8$ .

$- 2 (- 2 (- 9 + 81 - 32) - 3 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.2.5.2

Tambahkan $- 9$ dan $81$ .

$- 2 (- 2 (72 - 32) - 3 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.2.5.3

Kurangi $32$ dengan $72$ .

$- 2 (- 2 \cdot 40 - 3 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.3

Evaluasi $| \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} |$ .

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Langkah 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 3.3.1.1

Consider the corresponding sign chart.

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

Langkah 3.3.1.2

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

Langkah 3.3.1.3

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

$| \begin{array}{c} - 2 & 3 \\ 7 & - 9 \end{array} |$

Langkah 3.3.1.4

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

$7 | \begin{array}{c} - 2 & 3 \\ 7 & - 9 \end{array} |$

Langkah 3.3.1.5

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

$| \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} |$

Langkah 3.3.1.6

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

$9 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} |$

Langkah 3.3.1.7

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

$| \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |$

Langkah 3.3.1.8

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

$4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |$

Langkah 3.3.1.9

Add the terms together.

$- 2 (- 2 \cdot 40 - 3 (7 | \begin{array}{c} - 2 & 3 \\ 7 & - 9 \end{array} | + 9 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.3.2

Evaluasi $| \begin{array}{c} - 2 & 3 \\ 7 & - 9 \end{array} |$ .

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Langkah 3.3.2.1

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

$- 2 (- 2 \cdot 40 - 3 (7 (- 2 \cdot - 9 - 7 \cdot 3) + 9 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.3.2.2

Sederhanakan determinannya.

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Langkah 3.3.2.2.1

Sederhanakan setiap suku.

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Langkah 3.3.2.2.1.1

Kalikan $- 2$ dengan $- 9$ .

$- 2 (- 2 \cdot 40 - 3 (7 (18 - 7 \cdot 3) + 9 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.3.2.2.1.2

Kalikan $- 7$ dengan $3$ .

$- 2 (- 2 \cdot 40 - 3 (7 (18 - 21) + 9 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.3.2.2.2

Kurangi $21$ dengan $18$ .

$- 2 (- 2 \cdot 40 - 3 (7 \cdot - 3 + 9 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.3.3

Evaluasi $| \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} |$ .

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Langkah 3.3.3.1

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

$- 2 (- 2 \cdot 40 - 3 (7 \cdot - 3 + 9 (1 \cdot - 9 - (- 1 \cdot 3)) + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.3.3.2

Sederhanakan determinannya.

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Langkah 3.3.3.2.1

Sederhanakan setiap suku.

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Langkah 3.3.3.2.1.1

Kalikan $- 9$ dengan $1$ .

$- 2 (- 2 \cdot 40 - 3 (7 \cdot - 3 + 9 (- 9 - (- 1 \cdot 3)) + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.3.3.2.1.2

Kalikan $- (- 1 \cdot 3)$ .

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Langkah 3.3.3.2.1.2.1

Kalikan $- 1$ dengan $3$ .

$- 2 (- 2 \cdot 40 - 3 (7 \cdot - 3 + 9 (- 9 - - 3) + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.3.3.2.1.2.2

Kalikan $- 1$ dengan $- 3$ .

$- 2 (- 2 \cdot 40 - 3 (7 \cdot - 3 + 9 (- 9 + 3) + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.3.3.2.2

Tambahkan $- 9$ dan $3$ .

$- 2 (- 2 \cdot 40 - 3 (7 \cdot - 3 + 9 \cdot - 6 + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.3.4

Evaluasi $| \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |$ .

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Langkah 3.3.4.1

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

$- 2 (- 2 \cdot 40 - 3 (7 \cdot - 3 + 9 \cdot - 6 + 4 (1 \cdot 7 - - - 2)) - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.3.4.2

Sederhanakan determinannya.

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Langkah 3.3.4.2.1

Sederhanakan setiap suku.

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Langkah 3.3.4.2.1.1

Kalikan $7$ dengan $1$ .

$- 2 (- 2 \cdot 40 - 3 (7 \cdot - 3 + 9 \cdot - 6 + 4 (7 - - - 2)) - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.3.4.2.1.2

Kalikan $- - - 2$ .

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Langkah 3.3.4.2.1.2.1

Kalikan $- 1$ dengan $- 2$ .

$- 2 (- 2 \cdot 40 - 3 (7 \cdot - 3 + 9 \cdot - 6 + 4 (7 - 1 \cdot 2)) - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.3.4.2.1.2.2

Kalikan $- 1$ dengan $2$ .

$- 2 (- 2 \cdot 40 - 3 (7 \cdot - 3 + 9 \cdot - 6 + 4 (7 - 2)) - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.3.4.2.2

Kurangi $2$ dengan $7$ .

$- 2 (- 2 \cdot 40 - 3 (7 \cdot - 3 + 9 \cdot - 6 + 4 \cdot 5) - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.3.5

Sederhanakan determinannya.

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Langkah 3.3.5.1

Sederhanakan setiap suku.

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Langkah 3.3.5.1.1

Kalikan $7$ dengan $- 3$ .

$- 2 (- 2 \cdot 40 - 3 (- 21 + 9 \cdot - 6 + 4 \cdot 5) - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.3.5.1.2

Kalikan $9$ dengan $- 6$ .

$- 2 (- 2 \cdot 40 - 3 (- 21 - 54 + 4 \cdot 5) - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.3.5.1.3

Kalikan $4$ dengan $5$ .

$- 2 (- 2 \cdot 40 - 3 (- 21 - 54 + 20) - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.3.5.2

Kurangi $54$ dengan $- 21$ .

$- 2 (- 2 \cdot 40 - 3 (- 75 + 20) - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.3.5.3

Tambahkan $- 75$ dan $20$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.4

Evaluasi $| \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} |$ .

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Langkah 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 3.4.1.1

Consider the corresponding sign chart.

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

Langkah 3.4.1.2

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

Langkah 3.4.1.3

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

$| \begin{array}{c} - 2 & 3 \\ 3 & - 9 \end{array} |$

Langkah 3.4.1.4

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

$7 | \begin{array}{c} - 2 & 3 \\ 3 & - 9 \end{array} |$

Langkah 3.4.1.5

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

$| \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} |$

Langkah 3.4.1.6

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

$- 3 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} |$

Langkah 3.4.1.7

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

$| \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |$

Langkah 3.4.1.8

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

$4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |$

Langkah 3.4.1.9

Add the terms together.

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 (7 | \begin{array}{c} - 2 & 3 \\ 3 & - 9 \end{array} | - 3 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.4.2

Evaluasi $| \begin{array}{c} - 2 & 3 \\ 3 & - 9 \end{array} |$ .

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Langkah 3.4.2.1

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

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 (7 (- 2 \cdot - 9 - 3 \cdot 3) - 3 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.4.2.2

Sederhanakan determinannya.

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Langkah 3.4.2.2.1

Sederhanakan setiap suku.

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Langkah 3.4.2.2.1.1

Kalikan $- 2$ dengan $- 9$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 (7 (18 - 3 \cdot 3) - 3 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.4.2.2.1.2

Kalikan $- 3$ dengan $3$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 (7 (18 - 9) - 3 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.4.2.2.2

Kurangi $9$ dengan $18$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 (7 \cdot 9 - 3 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.4.3

Evaluasi $| \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} |$ .

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Langkah 3.4.3.1

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

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 (7 \cdot 9 - 3 (1 \cdot - 9 - (- 1 \cdot 3)) + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.4.3.2

Sederhanakan determinannya.

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Langkah 3.4.3.2.1

Sederhanakan setiap suku.

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Langkah 3.4.3.2.1.1

Kalikan $- 9$ dengan $1$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 (7 \cdot 9 - 3 (- 9 - (- 1 \cdot 3)) + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.4.3.2.1.2

Kalikan $- (- 1 \cdot 3)$ .

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Langkah 3.4.3.2.1.2.1

Kalikan $- 1$ dengan $3$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 (7 \cdot 9 - 3 (- 9 - - 3) + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.4.3.2.1.2.2

Kalikan $- 1$ dengan $- 3$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 (7 \cdot 9 - 3 (- 9 + 3) + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.4.3.2.2

Tambahkan $- 9$ dan $3$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 (7 \cdot 9 - 3 \cdot - 6 + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.4.4

Evaluasi $| \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |$ .

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Langkah 3.4.4.1

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

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 (7 \cdot 9 - 3 \cdot - 6 + 4 (1 \cdot 3 - - - 2)) - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.4.4.2

Sederhanakan determinannya.

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Langkah 3.4.4.2.1

Sederhanakan setiap suku.

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Langkah 3.4.4.2.1.1

Kalikan $3$ dengan $1$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 (7 \cdot 9 - 3 \cdot - 6 + 4 (3 - - - 2)) - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.4.4.2.1.2

Kalikan $- - - 2$ .

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Langkah 3.4.4.2.1.2.1

Kalikan $- 1$ dengan $- 2$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 (7 \cdot 9 - 3 \cdot - 6 + 4 (3 - 1 \cdot 2)) - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.4.4.2.1.2.2

Kalikan $- 1$ dengan $2$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 (7 \cdot 9 - 3 \cdot - 6 + 4 (3 - 2)) - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.4.4.2.2

Kurangi $2$ dengan $3$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 (7 \cdot 9 - 3 \cdot - 6 + 4 \cdot 1) - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.4.5

Sederhanakan determinannya.

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Langkah 3.4.5.1

Sederhanakan setiap suku.

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Langkah 3.4.5.1.1

Kalikan $7$ dengan $9$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 (63 - 3 \cdot - 6 + 4 \cdot 1) - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.4.5.1.2

Kalikan $- 3$ dengan $- 6$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 (63 + 18 + 4 \cdot 1) - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.4.5.1.3

Kalikan $4$ dengan $1$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 (63 + 18 + 4) - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.4.5.2

Tambahkan $63$ dan $18$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 (81 + 4) - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.4.5.3

Tambahkan $81$ dan $4$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.5

Evaluasi $| \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |$ .

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Langkah 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 3.5.1.1

Consider the corresponding sign chart.

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

Langkah 3.5.1.2

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

Langkah 3.5.1.3

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

$| \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |$

Langkah 3.5.1.4

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

$7 | \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |$

Langkah 3.5.1.5

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

$| \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |$

Langkah 3.5.1.6

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

$- 3 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |$

Langkah 3.5.1.7

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

$| \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |$

Langkah 3.5.1.8

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

$- 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |$

Langkah 3.5.1.9

Add the terms together.

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 (7 | \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} | - 3 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} | - 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |)) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.5.2

Evaluasi $| \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |$ .

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Langkah 3.5.2.1

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

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 (7 (- 2 \cdot 7 - 3 \cdot - 2) - 3 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} | - 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |)) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.5.2.2

Sederhanakan determinannya.

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Langkah 3.5.2.2.1

Sederhanakan setiap suku.

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Langkah 3.5.2.2.1.1

Kalikan $- 2$ dengan $7$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 (7 (- 14 - 3 \cdot - 2) - 3 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} | - 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |)) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.5.2.2.1.2

Kalikan $- 3$ dengan $- 2$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 (7 (- 14 + 6) - 3 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} | - 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |)) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.5.2.2.2

Tambahkan $- 14$ dan $6$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 (7 \cdot - 8 - 3 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} | - 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |)) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.5.3

Evaluasi $| \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |$ .

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Langkah 3.5.3.1

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

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 (7 \cdot - 8 - 3 (1 \cdot 7 - - - 2) - 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |)) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.5.3.2

Sederhanakan determinannya.

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Langkah 3.5.3.2.1

Sederhanakan setiap suku.

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Langkah 3.5.3.2.1.1

Kalikan $7$ dengan $1$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 (7 \cdot - 8 - 3 (7 - - - 2) - 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |)) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.5.3.2.1.2

Kalikan $- - - 2$ .

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Langkah 3.5.3.2.1.2.1

Kalikan $- 1$ dengan $- 2$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 (7 \cdot - 8 - 3 (7 - 1 \cdot 2) - 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |)) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.5.3.2.1.2.2

Kalikan $- 1$ dengan $2$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 (7 \cdot - 8 - 3 (7 - 2) - 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |)) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.5.3.2.2

Kurangi $2$ dengan $7$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 (7 \cdot - 8 - 3 \cdot 5 - 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |)) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.5.4

Evaluasi $| \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |$ .

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Langkah 3.5.4.1

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

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 (7 \cdot - 8 - 3 \cdot 5 - 9 (1 \cdot 3 - - - 2))) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.5.4.2

Sederhanakan determinannya.

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Langkah 3.5.4.2.1

Sederhanakan setiap suku.

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Langkah 3.5.4.2.1.1

Kalikan $3$ dengan $1$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 (7 \cdot - 8 - 3 \cdot 5 - 9 (3 - - - 2))) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.5.4.2.1.2

Kalikan $- - - 2$ .

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Langkah 3.5.4.2.1.2.1

Kalikan $- 1$ dengan $- 2$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 (7 \cdot - 8 - 3 \cdot 5 - 9 (3 - 1 \cdot 2))) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.5.4.2.1.2.2

Kalikan $- 1$ dengan $2$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 (7 \cdot - 8 - 3 \cdot 5 - 9 (3 - 2))) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.5.4.2.2

Kurangi $2$ dengan $3$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 (7 \cdot - 8 - 3 \cdot 5 - 9 \cdot 1)) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.5.5

Sederhanakan determinannya.

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Langkah 3.5.5.1

Sederhanakan setiap suku.

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Langkah 3.5.5.1.1

Kalikan $7$ dengan $- 8$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 (- 56 - 3 \cdot 5 - 9 \cdot 1)) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.5.5.1.2

Kalikan $- 3$ dengan $5$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 (- 56 - 15 - 9 \cdot 1)) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.5.5.1.3

Kalikan $- 9$ dengan $1$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 (- 56 - 15 - 9)) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.5.5.2

Kurangi $15$ dengan $- 56$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 (- 71 - 9)) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.5.5.3

Kurangi $9$ dengan $- 71$ .

$- 2 (- 2 \cdot 40 - 3 \cdot - 55 - 5 \cdot 85 - 7 \cdot - 80) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.6

Sederhanakan determinannya.

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Langkah 3.6.1

Sederhanakan setiap suku.

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Langkah 3.6.1.1

Kalikan $- 2$ dengan $40$ .

$- 2 (- 80 - 3 \cdot - 55 - 5 \cdot 85 - 7 \cdot - 80) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.6.1.2

Kalikan $- 3$ dengan $- 55$ .

$- 2 (- 80 + 165 - 5 \cdot 85 - 7 \cdot - 80) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.6.1.3

Kalikan $- 5$ dengan $85$ .

$- 2 (- 80 + 165 - 425 - 7 \cdot - 80) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.6.1.4

Kalikan $- 7$ dengan $- 80$ .

$- 2 (- 80 + 165 - 425 + 560) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.6.2

Tambahkan $- 80$ dan $165$ .

$- 2 (85 - 425 + 560) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.6.3

Kurangi $425$ dengan $85$ .

$- 2 (- 340 + 560) + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 3.6.4

Tambahkan $- 340$ dan $560$ .

$- 2 \cdot 220 + 0 + 1 | \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4

Evaluasi $| \begin{array}{c} 1 & - 2 & - 5 & 7 \\ 4 & 7 & - 9 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 7 & - 9 \end{array} |$ .

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Langkah 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 4.1.1

Consider the corresponding sign chart.

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

Langkah 4.1.2

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

Langkah 4.1.3

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

$| \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} |$

Langkah 4.1.4

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

$1 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} |$

Langkah 4.1.5

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

$| \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} |$

Langkah 4.1.6

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

$2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} |$

Langkah 4.1.7

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

$| \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} |$

Langkah 4.1.8

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

$- 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} |$

Langkah 4.1.9

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

$| \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |$

Langkah 4.1.10

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

$- 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |$

Langkah 4.1.11

Add the terms together.

$- 2 \cdot 220 + 0 + 1 (1 | \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} | + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.2

Evaluasi $| \begin{array}{c} 7 & - 9 & 4 \\ 1 & - 2 & 3 \\ - 1 & 7 & - 9 \end{array} |$ .

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Langkah 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 4.2.1.1

Consider the corresponding sign chart.

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

Langkah 4.2.1.2

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

Langkah 4.2.1.3

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

$| \begin{array}{c} - 2 & 3 \\ 7 & - 9 \end{array} |$

Langkah 4.2.1.4

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

$7 | \begin{array}{c} - 2 & 3 \\ 7 & - 9 \end{array} |$

Langkah 4.2.1.5

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

$| \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} |$

Langkah 4.2.1.6

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

$9 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} |$

Langkah 4.2.1.7

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

$| \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |$

Langkah 4.2.1.8

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

$4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |$

Langkah 4.2.1.9

Add the terms together.

$- 2 \cdot 220 + 0 + 1 (1 (7 | \begin{array}{c} - 2 & 3 \\ 7 & - 9 \end{array} | + 9 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |) + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.2.2

Evaluasi $| \begin{array}{c} - 2 & 3 \\ 7 & - 9 \end{array} |$ .

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Langkah 4.2.2.1

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

$- 2 \cdot 220 + 0 + 1 (1 (7 (- 2 \cdot - 9 - 7 \cdot 3) + 9 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |) + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.2.2.2

Sederhanakan determinannya.

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Langkah 4.2.2.2.1

Sederhanakan setiap suku.

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Langkah 4.2.2.2.1.1

Kalikan $- 2$ dengan $- 9$ .

$- 2 \cdot 220 + 0 + 1 (1 (7 (18 - 7 \cdot 3) + 9 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |) + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.2.2.2.1.2

Kalikan $- 7$ dengan $3$ .

$- 2 \cdot 220 + 0 + 1 (1 (7 (18 - 21) + 9 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |) + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.2.2.2.2

Kurangi $21$ dengan $18$ .

$- 2 \cdot 220 + 0 + 1 (1 (7 \cdot - 3 + 9 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |) + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.2.3

Evaluasi $| \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} |$ .

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Langkah 4.2.3.1

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

$- 2 \cdot 220 + 0 + 1 (1 (7 \cdot - 3 + 9 (1 \cdot - 9 - (- 1 \cdot 3)) + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |) + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.2.3.2

Sederhanakan determinannya.

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Langkah 4.2.3.2.1

Sederhanakan setiap suku.

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Langkah 4.2.3.2.1.1

Kalikan $- 9$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 (1 (7 \cdot - 3 + 9 (- 9 - (- 1 \cdot 3)) + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |) + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.2.3.2.1.2

Kalikan $- (- 1 \cdot 3)$ .

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Langkah 4.2.3.2.1.2.1

Kalikan $- 1$ dengan $3$ .

$- 2 \cdot 220 + 0 + 1 (1 (7 \cdot - 3 + 9 (- 9 - - 3) + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |) + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.2.3.2.1.2.2

Kalikan $- 1$ dengan $- 3$ .

$- 2 \cdot 220 + 0 + 1 (1 (7 \cdot - 3 + 9 (- 9 + 3) + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |) + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.2.3.2.2

Tambahkan $- 9$ dan $3$ .

$- 2 \cdot 220 + 0 + 1 (1 (7 \cdot - 3 + 9 \cdot - 6 + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |) + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.2.4

Evaluasi $| \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |$ .

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Langkah 4.2.4.1

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

$- 2 \cdot 220 + 0 + 1 (1 (7 \cdot - 3 + 9 \cdot - 6 + 4 (1 \cdot 7 - - - 2)) + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.2.4.2

Sederhanakan determinannya.

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Langkah 4.2.4.2.1

Sederhanakan setiap suku.

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Langkah 4.2.4.2.1.1

Kalikan $7$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 (1 (7 \cdot - 3 + 9 \cdot - 6 + 4 (7 - - - 2)) + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.2.4.2.1.2

Kalikan $- - - 2$ .

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Langkah 4.2.4.2.1.2.1

Kalikan $- 1$ dengan $- 2$ .

$- 2 \cdot 220 + 0 + 1 (1 (7 \cdot - 3 + 9 \cdot - 6 + 4 (7 - 1 \cdot 2)) + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.2.4.2.1.2.2

Kalikan $- 1$ dengan $2$ .

$- 2 \cdot 220 + 0 + 1 (1 (7 \cdot - 3 + 9 \cdot - 6 + 4 (7 - 2)) + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.2.4.2.2

Kurangi $2$ dengan $7$ .

$- 2 \cdot 220 + 0 + 1 (1 (7 \cdot - 3 + 9 \cdot - 6 + 4 \cdot 5) + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.2.5

Sederhanakan determinannya.

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Langkah 4.2.5.1

Sederhanakan setiap suku.

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Langkah 4.2.5.1.1

Kalikan $7$ dengan $- 3$ .

$- 2 \cdot 220 + 0 + 1 (1 (- 21 + 9 \cdot - 6 + 4 \cdot 5) + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.2.5.1.2

Kalikan $9$ dengan $- 6$ .

$- 2 \cdot 220 + 0 + 1 (1 (- 21 - 54 + 4 \cdot 5) + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.2.5.1.3

Kalikan $4$ dengan $5$ .

$- 2 \cdot 220 + 0 + 1 (1 (- 21 - 54 + 20) + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.2.5.2

Kurangi $54$ dengan $- 21$ .

$- 2 \cdot 220 + 0 + 1 (1 (- 75 + 20) + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.2.5.3

Tambahkan $- 75$ dan $20$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 | \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} | - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.3

Evaluasi $| \begin{array}{c} 4 & - 9 & 4 \\ 3 & - 2 & 3 \\ - 5 & 7 & - 9 \end{array} |$ .

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Langkah 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 4.3.1.1

Consider the corresponding sign chart.

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

Langkah 4.3.1.2

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

Langkah 4.3.1.3

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

$| \begin{array}{c} - 2 & 3 \\ 7 & - 9 \end{array} |$

Langkah 4.3.1.4

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

$4 | \begin{array}{c} - 2 & 3 \\ 7 & - 9 \end{array} |$

Langkah 4.3.1.5

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

$| \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} |$

Langkah 4.3.1.6

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

$9 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} |$

Langkah 4.3.1.7

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

$| \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |$

Langkah 4.3.1.8

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

$4 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |$

Langkah 4.3.1.9

Add the terms together.

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 (4 | \begin{array}{c} - 2 & 3 \\ 7 & - 9 \end{array} | + 9 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |) - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.3.2

Evaluasi $| \begin{array}{c} - 2 & 3 \\ 7 & - 9 \end{array} |$ .

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Langkah 4.3.2.1

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

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 (4 (- 2 \cdot - 9 - 7 \cdot 3) + 9 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |) - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.3.2.2

Sederhanakan determinannya.

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Langkah 4.3.2.2.1

Sederhanakan setiap suku.

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Langkah 4.3.2.2.1.1

Kalikan $- 2$ dengan $- 9$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 (4 (18 - 7 \cdot 3) + 9 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |) - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.3.2.2.1.2

Kalikan $- 7$ dengan $3$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 (4 (18 - 21) + 9 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |) - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.3.2.2.2

Kurangi $21$ dengan $18$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 (4 \cdot - 3 + 9 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |) - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.3.3

Evaluasi $| \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} |$ .

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Langkah 4.3.3.1

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

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 (4 \cdot - 3 + 9 (3 \cdot - 9 - (- 5 \cdot 3)) + 4 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |) - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.3.3.2

Sederhanakan determinannya.

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Langkah 4.3.3.2.1

Sederhanakan setiap suku.

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Langkah 4.3.3.2.1.1

Kalikan $3$ dengan $- 9$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 (4 \cdot - 3 + 9 (- 27 - (- 5 \cdot 3)) + 4 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |) - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.3.3.2.1.2

Kalikan $- (- 5 \cdot 3)$ .

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Langkah 4.3.3.2.1.2.1

Kalikan $- 5$ dengan $3$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 (4 \cdot - 3 + 9 (- 27 - - 15) + 4 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |) - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.3.3.2.1.2.2

Kalikan $- 1$ dengan $- 15$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 (4 \cdot - 3 + 9 (- 27 + 15) + 4 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |) - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.3.3.2.2

Tambahkan $- 27$ dan $15$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 (4 \cdot - 3 + 9 \cdot - 12 + 4 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |) - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.3.4

Evaluasi $| \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |$ .

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Langkah 4.3.4.1

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

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 (4 \cdot - 3 + 9 \cdot - 12 + 4 (3 \cdot 7 - (- 5 \cdot - 2))) - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.3.4.2

Sederhanakan determinannya.

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Langkah 4.3.4.2.1

Sederhanakan setiap suku.

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Langkah 4.3.4.2.1.1

Kalikan $3$ dengan $7$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 (4 \cdot - 3 + 9 \cdot - 12 + 4 (21 - (- 5 \cdot - 2))) - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.3.4.2.1.2

Kalikan $- (- 5 \cdot - 2)$ .

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Langkah 4.3.4.2.1.2.1

Kalikan $- 5$ dengan $- 2$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 (4 \cdot - 3 + 9 \cdot - 12 + 4 (21 - 1 \cdot 10)) - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.3.4.2.1.2.2

Kalikan $- 1$ dengan $10$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 (4 \cdot - 3 + 9 \cdot - 12 + 4 (21 - 10)) - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.3.4.2.2

Kurangi $10$ dengan $21$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 (4 \cdot - 3 + 9 \cdot - 12 + 4 \cdot 11) - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.3.5

Sederhanakan determinannya.

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Langkah 4.3.5.1

Sederhanakan setiap suku.

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Langkah 4.3.5.1.1

Kalikan $4$ dengan $- 3$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 (- 12 + 9 \cdot - 12 + 4 \cdot 11) - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.3.5.1.2

Kalikan $9$ dengan $- 12$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 (- 12 - 108 + 4 \cdot 11) - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.3.5.1.3

Kalikan $4$ dengan $11$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 (- 12 - 108 + 44) - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.3.5.2

Kurangi $108$ dengan $- 12$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 (- 120 + 44) - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.3.5.3

Tambahkan $- 120$ dan $44$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4

Evaluasi $| \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} |$ .

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Langkah 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 4.4.1.1

Consider the corresponding sign chart.

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

Langkah 4.4.1.2

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

Langkah 4.4.1.3

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

$| \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} |$

Langkah 4.4.1.4

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

$4 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} |$

Langkah 4.4.1.5

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

$| \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} |$

Langkah 4.4.1.6

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

$- 7 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} |$

Langkah 4.4.1.7

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

$| \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |$

Langkah 4.4.1.8

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

$4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |$

Langkah 4.4.1.9

Add the terms together.

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 (4 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4.2

Evaluasi $| \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} |$ .

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Langkah 4.4.2.1

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

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 (4 (1 \cdot - 9 - (- 1 \cdot 3)) - 7 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4.2.2

Sederhanakan determinannya.

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Langkah 4.4.2.2.1

Sederhanakan setiap suku.

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Langkah 4.4.2.2.1.1

Kalikan $- 9$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 (4 (- 9 - (- 1 \cdot 3)) - 7 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4.2.2.1.2

Kalikan $- (- 1 \cdot 3)$ .

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Langkah 4.4.2.2.1.2.1

Kalikan $- 1$ dengan $3$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 (4 (- 9 - - 3) - 7 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4.2.2.1.2.2

Kalikan $- 1$ dengan $- 3$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 (4 (- 9 + 3) - 7 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4.2.2.2

Tambahkan $- 9$ dan $3$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 (4 \cdot - 6 - 7 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4.3

Evaluasi $| \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} |$ .

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Langkah 4.4.3.1

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

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 (4 \cdot - 6 - 7 (3 \cdot - 9 - (- 5 \cdot 3)) + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4.3.2

Sederhanakan determinannya.

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Langkah 4.4.3.2.1

Sederhanakan setiap suku.

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Langkah 4.4.3.2.1.1

Kalikan $3$ dengan $- 9$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 (4 \cdot - 6 - 7 (- 27 - (- 5 \cdot 3)) + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4.3.2.1.2

Kalikan $- (- 5 \cdot 3)$ .

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Langkah 4.4.3.2.1.2.1

Kalikan $- 5$ dengan $3$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 (4 \cdot - 6 - 7 (- 27 - - 15) + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4.3.2.1.2.2

Kalikan $- 1$ dengan $- 15$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 (4 \cdot - 6 - 7 (- 27 + 15) + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4.3.2.2

Tambahkan $- 27$ dan $15$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 (4 \cdot - 6 - 7 \cdot - 12 + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4.4

Evaluasi $| \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |$ .

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Langkah 4.4.4.1

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

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 (4 \cdot - 6 - 7 \cdot - 12 + 4 (3 \cdot - 1 - (- 5 \cdot 1))) - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4.4.2

Sederhanakan determinannya.

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Langkah 4.4.4.2.1

Sederhanakan setiap suku.

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Langkah 4.4.4.2.1.1

Kalikan $3$ dengan $- 1$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 (4 \cdot - 6 - 7 \cdot - 12 + 4 (- 3 - (- 5 \cdot 1))) - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4.4.2.1.2

Kalikan $- (- 5 \cdot 1)$ .

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Langkah 4.4.4.2.1.2.1

Kalikan $- 5$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 (4 \cdot - 6 - 7 \cdot - 12 + 4 (- 3 - - 5)) - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4.4.2.1.2.2

Kalikan $- 1$ dengan $- 5$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 (4 \cdot - 6 - 7 \cdot - 12 + 4 (- 3 + 5)) - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4.4.2.2

Tambahkan $- 3$ dan $5$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 (4 \cdot - 6 - 7 \cdot - 12 + 4 \cdot 2) - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4.5

Sederhanakan determinannya.

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Langkah 4.4.5.1

Sederhanakan setiap suku.

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Langkah 4.4.5.1.1

Kalikan $4$ dengan $- 6$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 (- 24 - 7 \cdot - 12 + 4 \cdot 2) - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4.5.1.2

Kalikan $- 7$ dengan $- 12$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 (- 24 + 84 + 4 \cdot 2) - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4.5.1.3

Kalikan $4$ dengan $2$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 (- 24 + 84 + 8) - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4.5.2

Tambahkan $- 24$ dan $84$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 (60 + 8) - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.4.5.3

Tambahkan $60$ dan $8$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5

Evaluasi $| \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |$ .

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Langkah 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 4.5.1.1

Consider the corresponding sign chart.

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

Langkah 4.5.1.2

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

Langkah 4.5.1.3

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

$| \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |$

Langkah 4.5.1.4

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

$4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |$

Langkah 4.5.1.5

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

$| \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |$

Langkah 4.5.1.6

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

$- 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |$

Langkah 4.5.1.7

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

$| \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |$

Langkah 4.5.1.8

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

$- 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |$

Langkah 4.5.1.9

Add the terms together.

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 (4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} | - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} | - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5.2

Evaluasi $| \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |$ .

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Langkah 4.5.2.1

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

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 (4 (1 \cdot 7 - - - 2) - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} | - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5.2.2

Sederhanakan determinannya.

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Langkah 4.5.2.2.1

Sederhanakan setiap suku.

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Langkah 4.5.2.2.1.1

Kalikan $7$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 (4 (7 - - - 2) - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} | - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5.2.2.1.2

Kalikan $- - - 2$ .

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Langkah 4.5.2.2.1.2.1

Kalikan $- 1$ dengan $- 2$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 (4 (7 - 1 \cdot 2) - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} | - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5.2.2.1.2.2

Kalikan $- 1$ dengan $2$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 (4 (7 - 2) - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} | - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5.2.2.2

Kurangi $2$ dengan $7$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 (4 \cdot 5 - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} | - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5.3

Evaluasi $| \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |$ .

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Langkah 4.5.3.1

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

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 (4 \cdot 5 - 7 (3 \cdot 7 - (- 5 \cdot - 2)) - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5.3.2

Sederhanakan determinannya.

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Langkah 4.5.3.2.1

Sederhanakan setiap suku.

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Langkah 4.5.3.2.1.1

Kalikan $3$ dengan $7$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 (4 \cdot 5 - 7 (21 - (- 5 \cdot - 2)) - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5.3.2.1.2

Kalikan $- (- 5 \cdot - 2)$ .

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Langkah 4.5.3.2.1.2.1

Kalikan $- 5$ dengan $- 2$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 (4 \cdot 5 - 7 (21 - 1 \cdot 10) - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5.3.2.1.2.2

Kalikan $- 1$ dengan $10$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 (4 \cdot 5 - 7 (21 - 10) - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5.3.2.2

Kurangi $10$ dengan $21$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 (4 \cdot 5 - 7 \cdot 11 - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5.4

Evaluasi $| \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |$ .

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Langkah 4.5.4.1

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

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 (4 \cdot 5 - 7 \cdot 11 - 9 (3 \cdot - 1 - (- 5 \cdot 1)))) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5.4.2

Sederhanakan determinannya.

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Langkah 4.5.4.2.1

Sederhanakan setiap suku.

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Langkah 4.5.4.2.1.1

Kalikan $3$ dengan $- 1$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 (4 \cdot 5 - 7 \cdot 11 - 9 (- 3 - (- 5 \cdot 1)))) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5.4.2.1.2

Kalikan $- (- 5 \cdot 1)$ .

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Langkah 4.5.4.2.1.2.1

Kalikan $- 5$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 (4 \cdot 5 - 7 \cdot 11 - 9 (- 3 - - 5))) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5.4.2.1.2.2

Kalikan $- 1$ dengan $- 5$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 (4 \cdot 5 - 7 \cdot 11 - 9 (- 3 + 5))) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5.4.2.2

Tambahkan $- 3$ dan $5$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 (4 \cdot 5 - 7 \cdot 11 - 9 \cdot 2)) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5.5

Sederhanakan determinannya.

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Langkah 4.5.5.1

Sederhanakan setiap suku.

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Langkah 4.5.5.1.1

Kalikan $4$ dengan $5$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 (20 - 7 \cdot 11 - 9 \cdot 2)) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5.5.1.2

Kalikan $- 7$ dengan $11$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 (20 - 77 - 9 \cdot 2)) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5.5.1.3

Kalikan $- 9$ dengan $2$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 (20 - 77 - 18)) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5.5.2

Kurangi $77$ dengan $20$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 (- 57 - 18)) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.5.5.3

Kurangi $18$ dengan $- 57$ .

$- 2 \cdot 220 + 0 + 1 (1 \cdot - 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 \cdot - 75) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.6

Sederhanakan determinannya.

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Langkah 4.6.1

Sederhanakan setiap suku.

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Langkah 4.6.1.1

Kalikan $- 55$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 (- 55 + 2 \cdot - 76 - 5 \cdot 68 - 7 \cdot - 75) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.6.1.2

Kalikan $2$ dengan $- 76$ .

$- 2 \cdot 220 + 0 + 1 (- 55 - 152 - 5 \cdot 68 - 7 \cdot - 75) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.6.1.3

Kalikan $- 5$ dengan $68$ .

$- 2 \cdot 220 + 0 + 1 (- 55 - 152 - 340 - 7 \cdot - 75) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.6.1.4

Kalikan $- 7$ dengan $- 75$ .

$- 2 \cdot 220 + 0 + 1 (- 55 - 152 - 340 + 525) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.6.2

Kurangi $152$ dengan $- 55$ .

$- 2 \cdot 220 + 0 + 1 (- 207 - 340 + 525) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.6.3

Kurangi $340$ dengan $- 207$ .

$- 2 \cdot 220 + 0 + 1 (- 547 + 525) - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 4.6.4

Tambahkan $- 547$ dan $525$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 | \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} | - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5

Evaluasi $| \begin{array}{c} 1 & - 2 & 3 & 7 \\ 4 & 7 & 3 & 4 \\ 3 & 1 & - 2 & 3 \\ - 5 & - 1 & 3 & - 9 \end{array} |$ .

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Langkah 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 5.1.1

Consider the corresponding sign chart.

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

Langkah 5.1.2

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

Langkah 5.1.3

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

$| \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} |$

Langkah 5.1.4

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

$1 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} |$

Langkah 5.1.5

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

$| \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} |$

Langkah 5.1.6

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

$2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} |$

Langkah 5.1.7

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

$| \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} |$

Langkah 5.1.8

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

$3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} |$

Langkah 5.1.9

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

$| \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |$

Langkah 5.1.10

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

$- 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |$

Langkah 5.1.11

Add the terms together.

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 | \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} | + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.2

Evaluasi $| \begin{array}{c} 7 & 3 & 4 \\ 1 & - 2 & 3 \\ - 1 & 3 & - 9 \end{array} |$ .

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Langkah 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 5.2.1.1

Consider the corresponding sign chart.

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

Langkah 5.2.1.2

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

Langkah 5.2.1.3

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

$| \begin{array}{c} - 2 & 3 \\ 3 & - 9 \end{array} |$

Langkah 5.2.1.4

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

$7 | \begin{array}{c} - 2 & 3 \\ 3 & - 9 \end{array} |$

Langkah 5.2.1.5

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

$| \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} |$

Langkah 5.2.1.6

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

$- 3 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} |$

Langkah 5.2.1.7

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

$| \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |$

Langkah 5.2.1.8

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

$4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |$

Langkah 5.2.1.9

Add the terms together.

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 (7 | \begin{array}{c} - 2 & 3 \\ 3 & - 9 \end{array} | - 3 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.2.2

Evaluasi $| \begin{array}{c} - 2 & 3 \\ 3 & - 9 \end{array} |$ .

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Langkah 5.2.2.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 (7 (- 2 \cdot - 9 - 3 \cdot 3) - 3 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.2.2.2

Sederhanakan determinannya.

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Langkah 5.2.2.2.1

Sederhanakan setiap suku.

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Langkah 5.2.2.2.1.1

Kalikan $- 2$ dengan $- 9$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 (7 (18 - 3 \cdot 3) - 3 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.2.2.2.1.2

Kalikan $- 3$ dengan $3$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 (7 (18 - 9) - 3 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.2.2.2.2

Kurangi $9$ dengan $18$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 (7 \cdot 9 - 3 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.2.3

Evaluasi $| \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} |$ .

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Langkah 5.2.3.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 (7 \cdot 9 - 3 (1 \cdot - 9 - (- 1 \cdot 3)) + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.2.3.2

Sederhanakan determinannya.

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Langkah 5.2.3.2.1

Sederhanakan setiap suku.

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Langkah 5.2.3.2.1.1

Kalikan $- 9$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 (7 \cdot 9 - 3 (- 9 - (- 1 \cdot 3)) + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.2.3.2.1.2

Kalikan $- (- 1 \cdot 3)$ .

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Langkah 5.2.3.2.1.2.1

Kalikan $- 1$ dengan $3$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 (7 \cdot 9 - 3 (- 9 - - 3) + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.2.3.2.1.2.2

Kalikan $- 1$ dengan $- 3$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 (7 \cdot 9 - 3 (- 9 + 3) + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.2.3.2.2

Tambahkan $- 9$ dan $3$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 (7 \cdot 9 - 3 \cdot - 6 + 4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.2.4

Evaluasi $| \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |$ .

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Langkah 5.2.4.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 (7 \cdot 9 - 3 \cdot - 6 + 4 (1 \cdot 3 - - - 2)) + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.2.4.2

Sederhanakan determinannya.

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Langkah 5.2.4.2.1

Sederhanakan setiap suku.

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Langkah 5.2.4.2.1.1

Kalikan $3$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 (7 \cdot 9 - 3 \cdot - 6 + 4 (3 - - - 2)) + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.2.4.2.1.2

Kalikan $- - - 2$ .

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Langkah 5.2.4.2.1.2.1

Kalikan $- 1$ dengan $- 2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 (7 \cdot 9 - 3 \cdot - 6 + 4 (3 - 1 \cdot 2)) + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.2.4.2.1.2.2

Kalikan $- 1$ dengan $2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 (7 \cdot 9 - 3 \cdot - 6 + 4 (3 - 2)) + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.2.4.2.2

Kurangi $2$ dengan $3$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 (7 \cdot 9 - 3 \cdot - 6 + 4 \cdot 1) + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.2.5

Sederhanakan determinannya.

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Langkah 5.2.5.1

Sederhanakan setiap suku.

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Langkah 5.2.5.1.1

Kalikan $7$ dengan $9$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 (63 - 3 \cdot - 6 + 4 \cdot 1) + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.2.5.1.2

Kalikan $- 3$ dengan $- 6$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 (63 + 18 + 4 \cdot 1) + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.2.5.1.3

Kalikan $4$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 (63 + 18 + 4) + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.2.5.2

Tambahkan $63$ dan $18$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 (81 + 4) + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.2.5.3

Tambahkan $81$ dan $4$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 | \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} | + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.3

Evaluasi $| \begin{array}{c} 4 & 3 & 4 \\ 3 & - 2 & 3 \\ - 5 & 3 & - 9 \end{array} |$ .

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Langkah 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 5.3.1.1

Consider the corresponding sign chart.

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

Langkah 5.3.1.2

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

Langkah 5.3.1.3

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

$| \begin{array}{c} - 2 & 3 \\ 3 & - 9 \end{array} |$

Langkah 5.3.1.4

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

$4 | \begin{array}{c} - 2 & 3 \\ 3 & - 9 \end{array} |$

Langkah 5.3.1.5

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

$| \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} |$

Langkah 5.3.1.6

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

$- 3 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} |$

Langkah 5.3.1.7

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

$| \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |$

Langkah 5.3.1.8

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

$4 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |$

Langkah 5.3.1.9

Add the terms together.

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 (4 | \begin{array}{c} - 2 & 3 \\ 3 & - 9 \end{array} | - 3 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |) + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.3.2

Evaluasi $| \begin{array}{c} - 2 & 3 \\ 3 & - 9 \end{array} |$ .

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Langkah 5.3.2.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 (4 (- 2 \cdot - 9 - 3 \cdot 3) - 3 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |) + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.3.2.2

Sederhanakan determinannya.

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Langkah 5.3.2.2.1

Sederhanakan setiap suku.

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Langkah 5.3.2.2.1.1

Kalikan $- 2$ dengan $- 9$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 (4 (18 - 3 \cdot 3) - 3 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |) + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.3.2.2.1.2

Kalikan $- 3$ dengan $3$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 (4 (18 - 9) - 3 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |) + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.3.2.2.2

Kurangi $9$ dengan $18$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 (4 \cdot 9 - 3 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |) + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.3.3

Evaluasi $| \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} |$ .

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Langkah 5.3.3.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 (4 \cdot 9 - 3 (3 \cdot - 9 - (- 5 \cdot 3)) + 4 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |) + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.3.3.2

Sederhanakan determinannya.

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Langkah 5.3.3.2.1

Sederhanakan setiap suku.

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Langkah 5.3.3.2.1.1

Kalikan $3$ dengan $- 9$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 (4 \cdot 9 - 3 (- 27 - (- 5 \cdot 3)) + 4 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |) + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.3.3.2.1.2

Kalikan $- (- 5 \cdot 3)$ .

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Langkah 5.3.3.2.1.2.1

Kalikan $- 5$ dengan $3$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 (4 \cdot 9 - 3 (- 27 - - 15) + 4 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |) + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.3.3.2.1.2.2

Kalikan $- 1$ dengan $- 15$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 (4 \cdot 9 - 3 (- 27 + 15) + 4 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |) + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.3.3.2.2

Tambahkan $- 27$ dan $15$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 (4 \cdot 9 - 3 \cdot - 12 + 4 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |) + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.3.4

Evaluasi $| \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |$ .

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Langkah 5.3.4.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 (4 \cdot 9 - 3 \cdot - 12 + 4 (3 \cdot 3 - (- 5 \cdot - 2))) + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.3.4.2

Sederhanakan determinannya.

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Langkah 5.3.4.2.1

Sederhanakan setiap suku.

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Langkah 5.3.4.2.1.1

Kalikan $3$ dengan $3$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 (4 \cdot 9 - 3 \cdot - 12 + 4 (9 - (- 5 \cdot - 2))) + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.3.4.2.1.2

Kalikan $- (- 5 \cdot - 2)$ .

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Langkah 5.3.4.2.1.2.1

Kalikan $- 5$ dengan $- 2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 (4 \cdot 9 - 3 \cdot - 12 + 4 (9 - 1 \cdot 10)) + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.3.4.2.1.2.2

Kalikan $- 1$ dengan $10$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 (4 \cdot 9 - 3 \cdot - 12 + 4 (9 - 10)) + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.3.4.2.2

Kurangi $10$ dengan $9$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 (4 \cdot 9 - 3 \cdot - 12 + 4 \cdot - 1) + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.3.5

Sederhanakan determinannya.

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Langkah 5.3.5.1

Sederhanakan setiap suku.

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Langkah 5.3.5.1.1

Kalikan $4$ dengan $9$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 (36 - 3 \cdot - 12 + 4 \cdot - 1) + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.3.5.1.2

Kalikan $- 3$ dengan $- 12$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 (36 + 36 + 4 \cdot - 1) + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.3.5.1.3

Kalikan $4$ dengan $- 1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 (36 + 36 - 4) + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.3.5.2

Tambahkan $36$ dan $36$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 (72 - 4) + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.3.5.3

Kurangi $4$ dengan $72$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 | \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4

Evaluasi $| \begin{array}{c} 4 & 7 & 4 \\ 3 & 1 & 3 \\ - 5 & - 1 & - 9 \end{array} |$ .

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Langkah 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 5.4.1.1

Consider the corresponding sign chart.

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

Langkah 5.4.1.2

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

Langkah 5.4.1.3

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

$| \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} |$

Langkah 5.4.1.4

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

$4 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} |$

Langkah 5.4.1.5

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

$| \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} |$

Langkah 5.4.1.6

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

$- 7 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} |$

Langkah 5.4.1.7

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

$| \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |$

Langkah 5.4.1.8

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

$4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |$

Langkah 5.4.1.9

Add the terms together.

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 (4 | \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} | - 7 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4.2

Evaluasi $| \begin{array}{c} 1 & 3 \\ - 1 & - 9 \end{array} |$ .

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Langkah 5.4.2.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 (4 (1 \cdot - 9 - (- 1 \cdot 3)) - 7 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4.2.2

Sederhanakan determinannya.

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Langkah 5.4.2.2.1

Sederhanakan setiap suku.

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Langkah 5.4.2.2.1.1

Kalikan $- 9$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 (4 (- 9 - (- 1 \cdot 3)) - 7 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4.2.2.1.2

Kalikan $- (- 1 \cdot 3)$ .

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Langkah 5.4.2.2.1.2.1

Kalikan $- 1$ dengan $3$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 (4 (- 9 - - 3) - 7 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4.2.2.1.2.2

Kalikan $- 1$ dengan $- 3$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 (4 (- 9 + 3) - 7 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4.2.2.2

Tambahkan $- 9$ dan $3$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 (4 \cdot - 6 - 7 | \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} | + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4.3

Evaluasi $| \begin{array}{c} 3 & 3 \\ - 5 & - 9 \end{array} |$ .

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Langkah 5.4.3.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 (4 \cdot - 6 - 7 (3 \cdot - 9 - (- 5 \cdot 3)) + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4.3.2

Sederhanakan determinannya.

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Langkah 5.4.3.2.1

Sederhanakan setiap suku.

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Langkah 5.4.3.2.1.1

Kalikan $3$ dengan $- 9$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 (4 \cdot - 6 - 7 (- 27 - (- 5 \cdot 3)) + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4.3.2.1.2

Kalikan $- (- 5 \cdot 3)$ .

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Langkah 5.4.3.2.1.2.1

Kalikan $- 5$ dengan $3$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 (4 \cdot - 6 - 7 (- 27 - - 15) + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4.3.2.1.2.2

Kalikan $- 1$ dengan $- 15$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 (4 \cdot - 6 - 7 (- 27 + 15) + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4.3.2.2

Tambahkan $- 27$ dan $15$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 (4 \cdot - 6 - 7 \cdot - 12 + 4 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4.4

Evaluasi $| \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |$ .

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Langkah 5.4.4.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 (4 \cdot - 6 - 7 \cdot - 12 + 4 (3 \cdot - 1 - (- 5 \cdot 1))) - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4.4.2

Sederhanakan determinannya.

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Langkah 5.4.4.2.1

Sederhanakan setiap suku.

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Langkah 5.4.4.2.1.1

Kalikan $3$ dengan $- 1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 (4 \cdot - 6 - 7 \cdot - 12 + 4 (- 3 - (- 5 \cdot 1))) - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4.4.2.1.2

Kalikan $- (- 5 \cdot 1)$ .

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Langkah 5.4.4.2.1.2.1

Kalikan $- 5$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 (4 \cdot - 6 - 7 \cdot - 12 + 4 (- 3 - - 5)) - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4.4.2.1.2.2

Kalikan $- 1$ dengan $- 5$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 (4 \cdot - 6 - 7 \cdot - 12 + 4 (- 3 + 5)) - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4.4.2.2

Tambahkan $- 3$ dan $5$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 (4 \cdot - 6 - 7 \cdot - 12 + 4 \cdot 2) - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4.5

Sederhanakan determinannya.

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Langkah 5.4.5.1

Sederhanakan setiap suku.

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Langkah 5.4.5.1.1

Kalikan $4$ dengan $- 6$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 (- 24 - 7 \cdot - 12 + 4 \cdot 2) - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4.5.1.2

Kalikan $- 7$ dengan $- 12$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 (- 24 + 84 + 4 \cdot 2) - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4.5.1.3

Kalikan $4$ dengan $2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 (- 24 + 84 + 8) - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4.5.2

Tambahkan $- 24$ dan $84$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 (60 + 8) - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.4.5.3

Tambahkan $60$ dan $8$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5

Evaluasi $| \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |$ .

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Langkah 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 5.5.1.1

Consider the corresponding sign chart.

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

Langkah 5.5.1.2

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

Langkah 5.5.1.3

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

$| \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |$

Langkah 5.5.1.4

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

$4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |$

Langkah 5.5.1.5

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

$| \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |$

Langkah 5.5.1.6

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

$- 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |$

Langkah 5.5.1.7

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

$| \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |$

Langkah 5.5.1.8

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

$3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |$

Langkah 5.5.1.9

Add the terms together.

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 (4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} | - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} | + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5.2

Evaluasi $| \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |$ .

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Langkah 5.5.2.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 (4 (1 \cdot 3 - - - 2) - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} | + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5.2.2

Sederhanakan determinannya.

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Langkah 5.5.2.2.1

Sederhanakan setiap suku.

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Langkah 5.5.2.2.1.1

Kalikan $3$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 (4 (3 - - - 2) - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} | + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5.2.2.1.2

Kalikan $- - - 2$ .

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Langkah 5.5.2.2.1.2.1

Kalikan $- 1$ dengan $- 2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 (4 (3 - 1 \cdot 2) - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} | + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5.2.2.1.2.2

Kalikan $- 1$ dengan $2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 (4 (3 - 2) - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} | + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5.2.2.2

Kurangi $2$ dengan $3$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 (4 \cdot 1 - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} | + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5.3

Evaluasi $| \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |$ .

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Langkah 5.5.3.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 (4 \cdot 1 - 7 (3 \cdot 3 - (- 5 \cdot - 2)) + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5.3.2

Sederhanakan determinannya.

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Langkah 5.5.3.2.1

Sederhanakan setiap suku.

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Langkah 5.5.3.2.1.1

Kalikan $3$ dengan $3$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 (4 \cdot 1 - 7 (9 - (- 5 \cdot - 2)) + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5.3.2.1.2

Kalikan $- (- 5 \cdot - 2)$ .

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Langkah 5.5.3.2.1.2.1

Kalikan $- 5$ dengan $- 2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 (4 \cdot 1 - 7 (9 - 1 \cdot 10) + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5.3.2.1.2.2

Kalikan $- 1$ dengan $10$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 (4 \cdot 1 - 7 (9 - 10) + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5.3.2.2

Kurangi $10$ dengan $9$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 (4 \cdot 1 - 7 \cdot - 1 + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |)) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5.4

Evaluasi $| \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |$ .

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Langkah 5.5.4.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 (4 \cdot 1 - 7 \cdot - 1 + 3 (3 \cdot - 1 - (- 5 \cdot 1)))) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5.4.2

Sederhanakan determinannya.

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Langkah 5.5.4.2.1

Sederhanakan setiap suku.

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Langkah 5.5.4.2.1.1

Kalikan $3$ dengan $- 1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 (4 \cdot 1 - 7 \cdot - 1 + 3 (- 3 - (- 5 \cdot 1)))) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5.4.2.1.2

Kalikan $- (- 5 \cdot 1)$ .

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Langkah 5.5.4.2.1.2.1

Kalikan $- 5$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 (4 \cdot 1 - 7 \cdot - 1 + 3 (- 3 - - 5))) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5.4.2.1.2.2

Kalikan $- 1$ dengan $- 5$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 (4 \cdot 1 - 7 \cdot - 1 + 3 (- 3 + 5))) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5.4.2.2

Tambahkan $- 3$ dan $5$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 (4 \cdot 1 - 7 \cdot - 1 + 3 \cdot 2)) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5.5

Sederhanakan determinannya.

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Langkah 5.5.5.1

Sederhanakan setiap suku.

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Langkah 5.5.5.1.1

Kalikan $4$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 (4 - 7 \cdot - 1 + 3 \cdot 2)) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5.5.1.2

Kalikan $- 7$ dengan $- 1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 (4 + 7 + 3 \cdot 2)) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5.5.1.3

Kalikan $3$ dengan $2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 (4 + 7 + 6)) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5.5.2

Tambahkan $4$ dan $7$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 (11 + 6)) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.5.5.3

Tambahkan $11$ dan $6$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (1 \cdot 85 + 2 \cdot 68 + 3 \cdot 68 - 7 \cdot 17) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.6

Sederhanakan determinannya.

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Langkah 5.6.1

Sederhanakan setiap suku.

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Langkah 5.6.1.1

Kalikan $85$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (85 + 2 \cdot 68 + 3 \cdot 68 - 7 \cdot 17) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.6.1.2

Kalikan $2$ dengan $68$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (85 + 136 + 3 \cdot 68 - 7 \cdot 17) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.6.1.3

Kalikan $3$ dengan $68$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (85 + 136 + 204 - 7 \cdot 17) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.6.1.4

Kalikan $- 7$ dengan $17$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (85 + 136 + 204 - 119) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.6.2

Tambahkan $85$ dan $136$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (221 + 204 - 119) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.6.3

Tambahkan $221$ dan $204$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 (425 - 119) - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 5.6.4

Kurangi $119$ dengan $425$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 | \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$

Langkah 6

Evaluasi $| \begin{array}{c} 1 & - 2 & 3 & - 5 \\ 4 & 7 & 3 & - 9 \\ 3 & 1 & - 2 & - 2 \\ - 5 & - 1 & 3 & 7 \end{array} |$ .

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Langkah 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 6.1.1

Consider the corresponding sign chart.

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

Langkah 6.1.2

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

Langkah 6.1.3

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

$| \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |$

Langkah 6.1.4

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

$1 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |$

Langkah 6.1.5

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

$| \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} |$

Langkah 6.1.6

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

$2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} |$

Langkah 6.1.7

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

$| \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |$

Langkah 6.1.8

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

$3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |$

Langkah 6.1.9

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

$| \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |$

Langkah 6.1.10

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

$5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |$

Langkah 6.1.11

Add the terms together.

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 | \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} | + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.2

Evaluasi $| \begin{array}{c} 7 & 3 & - 9 \\ 1 & - 2 & - 2 \\ - 1 & 3 & 7 \end{array} |$ .

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Langkah 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 6.2.1.1

Consider the corresponding sign chart.

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

Langkah 6.2.1.2

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

Langkah 6.2.1.3

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

$| \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |$

Langkah 6.2.1.4

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

$7 | \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |$

Langkah 6.2.1.5

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

$| \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |$

Langkah 6.2.1.6

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

$- 3 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |$

Langkah 6.2.1.7

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

$| \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |$

Langkah 6.2.1.8

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

$- 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |$

Langkah 6.2.1.9

Add the terms together.

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 (7 | \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} | - 3 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} | - 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.2.2

Evaluasi $| \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |$ .

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Langkah 6.2.2.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 (7 (- 2 \cdot 7 - 3 \cdot - 2) - 3 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} | - 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.2.2.2

Sederhanakan determinannya.

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Langkah 6.2.2.2.1

Sederhanakan setiap suku.

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Langkah 6.2.2.2.1.1

Kalikan $- 2$ dengan $7$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 (7 (- 14 - 3 \cdot - 2) - 3 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} | - 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.2.2.2.1.2

Kalikan $- 3$ dengan $- 2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 (7 (- 14 + 6) - 3 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} | - 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.2.2.2.2

Tambahkan $- 14$ dan $6$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 (7 \cdot - 8 - 3 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} | - 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.2.3

Evaluasi $| \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |$ .

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Langkah 6.2.3.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 (7 \cdot - 8 - 3 (1 \cdot 7 - - - 2) - 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.2.3.2

Sederhanakan determinannya.

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Langkah 6.2.3.2.1

Sederhanakan setiap suku.

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Langkah 6.2.3.2.1.1

Kalikan $7$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 (7 \cdot - 8 - 3 (7 - - - 2) - 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.2.3.2.1.2

Kalikan $- - - 2$ .

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Langkah 6.2.3.2.1.2.1

Kalikan $- 1$ dengan $- 2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 (7 \cdot - 8 - 3 (7 - 1 \cdot 2) - 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.2.3.2.1.2.2

Kalikan $- 1$ dengan $2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 (7 \cdot - 8 - 3 (7 - 2) - 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.2.3.2.2

Kurangi $2$ dengan $7$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 (7 \cdot - 8 - 3 \cdot 5 - 9 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |) + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.2.4

Evaluasi $| \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |$ .

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Langkah 6.2.4.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 (7 \cdot - 8 - 3 \cdot 5 - 9 (1 \cdot 3 - - - 2)) + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.2.4.2

Sederhanakan determinannya.

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Langkah 6.2.4.2.1

Sederhanakan setiap suku.

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Langkah 6.2.4.2.1.1

Kalikan $3$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 (7 \cdot - 8 - 3 \cdot 5 - 9 (3 - - - 2)) + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.2.4.2.1.2

Kalikan $- - - 2$ .

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Langkah 6.2.4.2.1.2.1

Kalikan $- 1$ dengan $- 2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 (7 \cdot - 8 - 3 \cdot 5 - 9 (3 - 1 \cdot 2)) + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.2.4.2.1.2.2

Kalikan $- 1$ dengan $2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 (7 \cdot - 8 - 3 \cdot 5 - 9 (3 - 2)) + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.2.4.2.2

Kurangi $2$ dengan $3$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 (7 \cdot - 8 - 3 \cdot 5 - 9 \cdot 1) + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.2.5

Sederhanakan determinannya.

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Langkah 6.2.5.1

Sederhanakan setiap suku.

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Langkah 6.2.5.1.1

Kalikan $7$ dengan $- 8$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 (- 56 - 3 \cdot 5 - 9 \cdot 1) + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.2.5.1.2

Kalikan $- 3$ dengan $5$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 (- 56 - 15 - 9 \cdot 1) + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.2.5.1.3

Kalikan $- 9$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 (- 56 - 15 - 9) + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.2.5.2

Kurangi $15$ dengan $- 56$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 (- 71 - 9) + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.2.5.3

Kurangi $9$ dengan $- 71$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 | \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} | + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.3

Evaluasi $| \begin{array}{c} 4 & 3 & - 9 \\ 3 & - 2 & - 2 \\ - 5 & 3 & 7 \end{array} |$ .

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Langkah 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 6.3.1.1

Consider the corresponding sign chart.

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

Langkah 6.3.1.2

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

Langkah 6.3.1.3

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

$| \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |$

Langkah 6.3.1.4

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

$4 | \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |$

Langkah 6.3.1.5

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

$| \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |$

Langkah 6.3.1.6

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

$- 3 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |$

Langkah 6.3.1.7

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

$| \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |$

Langkah 6.3.1.8

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

$- 9 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |$

Langkah 6.3.1.9

Add the terms together.

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 (4 | \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} | - 3 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} | - 9 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |) + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.3.2

Evaluasi $| \begin{array}{c} - 2 & - 2 \\ 3 & 7 \end{array} |$ .

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Langkah 6.3.2.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 (4 (- 2 \cdot 7 - 3 \cdot - 2) - 3 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} | - 9 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |) + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.3.2.2

Sederhanakan determinannya.

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Langkah 6.3.2.2.1

Sederhanakan setiap suku.

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Langkah 6.3.2.2.1.1

Kalikan $- 2$ dengan $7$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 (4 (- 14 - 3 \cdot - 2) - 3 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} | - 9 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |) + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.3.2.2.1.2

Kalikan $- 3$ dengan $- 2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 (4 (- 14 + 6) - 3 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} | - 9 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |) + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.3.2.2.2

Tambahkan $- 14$ dan $6$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 (4 \cdot - 8 - 3 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} | - 9 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |) + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.3.3

Evaluasi $| \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |$ .

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Langkah 6.3.3.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 (4 \cdot - 8 - 3 (3 \cdot 7 - (- 5 \cdot - 2)) - 9 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |) + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.3.3.2

Sederhanakan determinannya.

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Langkah 6.3.3.2.1

Sederhanakan setiap suku.

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Langkah 6.3.3.2.1.1

Kalikan $3$ dengan $7$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 (4 \cdot - 8 - 3 (21 - (- 5 \cdot - 2)) - 9 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |) + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.3.3.2.1.2

Kalikan $- (- 5 \cdot - 2)$ .

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Langkah 6.3.3.2.1.2.1

Kalikan $- 5$ dengan $- 2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 (4 \cdot - 8 - 3 (21 - 1 \cdot 10) - 9 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |) + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.3.3.2.1.2.2

Kalikan $- 1$ dengan $10$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 (4 \cdot - 8 - 3 (21 - 10) - 9 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |) + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.3.3.2.2

Kurangi $10$ dengan $21$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 (4 \cdot - 8 - 3 \cdot 11 - 9 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |) + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.3.4

Evaluasi $| \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |$ .

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Langkah 6.3.4.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 (4 \cdot - 8 - 3 \cdot 11 - 9 (3 \cdot 3 - (- 5 \cdot - 2))) + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.3.4.2

Sederhanakan determinannya.

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Langkah 6.3.4.2.1

Sederhanakan setiap suku.

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Langkah 6.3.4.2.1.1

Kalikan $3$ dengan $3$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 (4 \cdot - 8 - 3 \cdot 11 - 9 (9 - (- 5 \cdot - 2))) + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.3.4.2.1.2

Kalikan $- (- 5 \cdot - 2)$ .

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Langkah 6.3.4.2.1.2.1

Kalikan $- 5$ dengan $- 2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 (4 \cdot - 8 - 3 \cdot 11 - 9 (9 - 1 \cdot 10)) + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.3.4.2.1.2.2

Kalikan $- 1$ dengan $10$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 (4 \cdot - 8 - 3 \cdot 11 - 9 (9 - 10)) + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.3.4.2.2

Kurangi $10$ dengan $9$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 (4 \cdot - 8 - 3 \cdot 11 - 9 \cdot - 1) + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.3.5

Sederhanakan determinannya.

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Langkah 6.3.5.1

Sederhanakan setiap suku.

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Langkah 6.3.5.1.1

Kalikan $4$ dengan $- 8$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 (- 32 - 3 \cdot 11 - 9 \cdot - 1) + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.3.5.1.2

Kalikan $- 3$ dengan $11$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 (- 32 - 33 - 9 \cdot - 1) + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.3.5.1.3

Kalikan $- 9$ dengan $- 1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 (- 32 - 33 + 9) + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.3.5.2

Kurangi $33$ dengan $- 32$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 (- 65 + 9) + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.3.5.3

Tambahkan $- 65$ dan $9$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 | \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} | + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4

Evaluasi $| \begin{array}{c} 4 & 7 & - 9 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 7 \end{array} |$ .

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Langkah 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 6.4.1.1

Consider the corresponding sign chart.

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

Langkah 6.4.1.2

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

Langkah 6.4.1.3

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

$| \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |$

Langkah 6.4.1.4

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

$4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |$

Langkah 6.4.1.5

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

$| \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |$

Langkah 6.4.1.6

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

$- 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |$

Langkah 6.4.1.7

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

$| \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |$

Langkah 6.4.1.8

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

$- 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |$

Langkah 6.4.1.9

Add the terms together.

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 (4 | \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} | - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} | - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4.2

Evaluasi $| \begin{array}{c} 1 & - 2 \\ - 1 & 7 \end{array} |$ .

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Langkah 6.4.2.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 (4 (1 \cdot 7 - - - 2) - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} | - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4.2.2

Sederhanakan determinannya.

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Langkah 6.4.2.2.1

Sederhanakan setiap suku.

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Langkah 6.4.2.2.1.1

Kalikan $7$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 (4 (7 - - - 2) - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} | - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4.2.2.1.2

Kalikan $- - - 2$ .

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Langkah 6.4.2.2.1.2.1

Kalikan $- 1$ dengan $- 2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 (4 (7 - 1 \cdot 2) - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} | - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4.2.2.1.2.2

Kalikan $- 1$ dengan $2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 (4 (7 - 2) - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} | - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4.2.2.2

Kurangi $2$ dengan $7$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 (4 \cdot 5 - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} | - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4.3

Evaluasi $| \begin{array}{c} 3 & - 2 \\ - 5 & 7 \end{array} |$ .

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Langkah 6.4.3.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 (4 \cdot 5 - 7 (3 \cdot 7 - (- 5 \cdot - 2)) - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4.3.2

Sederhanakan determinannya.

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Langkah 6.4.3.2.1

Sederhanakan setiap suku.

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Langkah 6.4.3.2.1.1

Kalikan $3$ dengan $7$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 (4 \cdot 5 - 7 (21 - (- 5 \cdot - 2)) - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4.3.2.1.2

Kalikan $- (- 5 \cdot - 2)$ .

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Langkah 6.4.3.2.1.2.1

Kalikan $- 5$ dengan $- 2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 (4 \cdot 5 - 7 (21 - 1 \cdot 10) - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4.3.2.1.2.2

Kalikan $- 1$ dengan $10$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 (4 \cdot 5 - 7 (21 - 10) - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4.3.2.2

Kurangi $10$ dengan $21$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 (4 \cdot 5 - 7 \cdot 11 - 9 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |) + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4.4

Evaluasi $| \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |$ .

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Langkah 6.4.4.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 (4 \cdot 5 - 7 \cdot 11 - 9 (3 \cdot - 1 - (- 5 \cdot 1))) + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4.4.2

Sederhanakan determinannya.

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Langkah 6.4.4.2.1

Sederhanakan setiap suku.

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Langkah 6.4.4.2.1.1

Kalikan $3$ dengan $- 1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 (4 \cdot 5 - 7 \cdot 11 - 9 (- 3 - (- 5 \cdot 1))) + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4.4.2.1.2

Kalikan $- (- 5 \cdot 1)$ .

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Langkah 6.4.4.2.1.2.1

Kalikan $- 5$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 (4 \cdot 5 - 7 \cdot 11 - 9 (- 3 - - 5)) + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4.4.2.1.2.2

Kalikan $- 1$ dengan $- 5$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 (4 \cdot 5 - 7 \cdot 11 - 9 (- 3 + 5)) + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4.4.2.2

Tambahkan $- 3$ dan $5$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 (4 \cdot 5 - 7 \cdot 11 - 9 \cdot 2) + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4.5

Sederhanakan determinannya.

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Langkah 6.4.5.1

Sederhanakan setiap suku.

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Langkah 6.4.5.1.1

Kalikan $4$ dengan $5$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 (20 - 7 \cdot 11 - 9 \cdot 2) + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4.5.1.2

Kalikan $- 7$ dengan $11$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 (20 - 77 - 9 \cdot 2) + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4.5.1.3

Kalikan $- 9$ dengan $2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 (20 - 77 - 18) + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4.5.2

Kurangi $77$ dengan $20$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 (- 57 - 18) + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.4.5.3

Kurangi $18$ dengan $- 57$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 | \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |)$

Langkah 6.5

Evaluasi $| \begin{array}{c} 4 & 7 & 3 \\ 3 & 1 & - 2 \\ - 5 & - 1 & 3 \end{array} |$ .

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Langkah 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 6.5.1.1

Consider the corresponding sign chart.

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

Langkah 6.5.1.2

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

Langkah 6.5.1.3

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

$| \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |$

Langkah 6.5.1.4

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

$4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |$

Langkah 6.5.1.5

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

$| \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |$

Langkah 6.5.1.6

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

$- 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |$

Langkah 6.5.1.7

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

$| \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |$

Langkah 6.5.1.8

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

$3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |$

Langkah 6.5.1.9

Add the terms together.

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 (4 | \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} | - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} | + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |))$

Langkah 6.5.2

Evaluasi $| \begin{array}{c} 1 & - 2 \\ - 1 & 3 \end{array} |$ .

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Langkah 6.5.2.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 (4 (1 \cdot 3 - - - 2) - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} | + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |))$

Langkah 6.5.2.2

Sederhanakan determinannya.

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Langkah 6.5.2.2.1

Sederhanakan setiap suku.

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Langkah 6.5.2.2.1.1

Kalikan $3$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 (4 (3 - - - 2) - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} | + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |))$

Langkah 6.5.2.2.1.2

Kalikan $- - - 2$ .

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Langkah 6.5.2.2.1.2.1

Kalikan $- 1$ dengan $- 2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 (4 (3 - 1 \cdot 2) - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} | + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |))$

Langkah 6.5.2.2.1.2.2

Kalikan $- 1$ dengan $2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 (4 (3 - 2) - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} | + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |))$

Langkah 6.5.2.2.2

Kurangi $2$ dengan $3$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 (4 \cdot 1 - 7 | \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} | + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |))$

Langkah 6.5.3

Evaluasi $| \begin{array}{c} 3 & - 2 \\ - 5 & 3 \end{array} |$ .

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Langkah 6.5.3.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 (4 \cdot 1 - 7 (3 \cdot 3 - (- 5 \cdot - 2)) + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |))$

Langkah 6.5.3.2

Sederhanakan determinannya.

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Langkah 6.5.3.2.1

Sederhanakan setiap suku.

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Langkah 6.5.3.2.1.1

Kalikan $3$ dengan $3$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 (4 \cdot 1 - 7 (9 - (- 5 \cdot - 2)) + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |))$

Langkah 6.5.3.2.1.2

Kalikan $- (- 5 \cdot - 2)$ .

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Langkah 6.5.3.2.1.2.1

Kalikan $- 5$ dengan $- 2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 (4 \cdot 1 - 7 (9 - 1 \cdot 10) + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |))$

Langkah 6.5.3.2.1.2.2

Kalikan $- 1$ dengan $10$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 (4 \cdot 1 - 7 (9 - 10) + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |))$

Langkah 6.5.3.2.2

Kurangi $10$ dengan $9$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 (4 \cdot 1 - 7 \cdot - 1 + 3 | \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |))$

Langkah 6.5.4

Evaluasi $| \begin{array}{c} 3 & 1 \\ - 5 & - 1 \end{array} |$ .

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Langkah 6.5.4.1

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

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 (4 \cdot 1 - 7 \cdot - 1 + 3 (3 \cdot - 1 - (- 5 \cdot 1))))$

Langkah 6.5.4.2

Sederhanakan determinannya.

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Langkah 6.5.4.2.1

Sederhanakan setiap suku.

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Langkah 6.5.4.2.1.1

Kalikan $3$ dengan $- 1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 (4 \cdot 1 - 7 \cdot - 1 + 3 (- 3 - (- 5 \cdot 1))))$

Langkah 6.5.4.2.1.2

Kalikan $- (- 5 \cdot 1)$ .

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Langkah 6.5.4.2.1.2.1

Kalikan $- 5$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 (4 \cdot 1 - 7 \cdot - 1 + 3 (- 3 - - 5)))$

Langkah 6.5.4.2.1.2.2

Kalikan $- 1$ dengan $- 5$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 (4 \cdot 1 - 7 \cdot - 1 + 3 (- 3 + 5)))$

Langkah 6.5.4.2.2

Tambahkan $- 3$ dan $5$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 (4 \cdot 1 - 7 \cdot - 1 + 3 \cdot 2))$

Langkah 6.5.5

Sederhanakan determinannya.

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Langkah 6.5.5.1

Sederhanakan setiap suku.

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Langkah 6.5.5.1.1

Kalikan $4$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 (4 - 7 \cdot - 1 + 3 \cdot 2))$

Langkah 6.5.5.1.2

Kalikan $- 7$ dengan $- 1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 (4 + 7 + 3 \cdot 2))$

Langkah 6.5.5.1.3

Kalikan $3$ dengan $2$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 (4 + 7 + 6))$

Langkah 6.5.5.2

Tambahkan $4$ dan $7$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 (11 + 6))$

Langkah 6.5.5.3

Tambahkan $11$ dan $6$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (1 \cdot - 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 \cdot 17)$

Langkah 6.6

Sederhanakan determinannya.

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Langkah 6.6.1

Sederhanakan setiap suku.

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Langkah 6.6.1.1

Kalikan $- 80$ dengan $1$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (- 80 + 2 \cdot - 56 + 3 \cdot - 75 + 5 \cdot 17)$

Langkah 6.6.1.2

Kalikan $2$ dengan $- 56$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (- 80 - 112 + 3 \cdot - 75 + 5 \cdot 17)$

Langkah 6.6.1.3

Kalikan $3$ dengan $- 75$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (- 80 - 112 - 225 + 5 \cdot 17)$

Langkah 6.6.1.4

Kalikan $5$ dengan $17$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (- 80 - 112 - 225 + 85)$

Langkah 6.6.2

Kurangi $112$ dengan $- 80$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (- 192 - 225 + 85)$

Langkah 6.6.3

Kurangi $225$ dengan $- 192$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 (- 417 + 85)$

Langkah 6.6.4

Tambahkan $- 417$ dan $85$ .

$- 2 \cdot 220 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 \cdot - 332$

Langkah 7

Sederhanakan determinannya.

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Langkah 7.1

Sederhanakan setiap suku.

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Langkah 7.1.1

Kalikan $- 2$ dengan $220$ .

$- 440 + 0 + 1 \cdot - 22 - 5 \cdot 306 - 6 \cdot - 332$

Langkah 7.1.2

Kalikan $- 22$ dengan $1$ .

$- 440 + 0 - 22 - 5 \cdot 306 - 6 \cdot - 332$

Langkah 7.1.3

Kalikan $- 5$ dengan $306$ .

$- 440 + 0 - 22 - 1530 - 6 \cdot - 332$

Langkah 7.1.4

Kalikan $- 6$ dengan $- 332$ .

$- 440 + 0 - 22 - 1530 + 1992$

Langkah 7.2

Tambahkan $- 440$ dan $0$ .

$- 440 - 22 - 1530 + 1992$

Langkah 7.3

Kurangi $22$ dengan $- 440$ .

$- 462 - 1530 + 1992$

Langkah 7.4

Kurangi $1530$ dengan $- 462$ .

$- 1992 + 1992$

Langkah 7.5

Tambahkan $- 1992$ dan $1992$ .

$0$