Matemática discreta Exemplos

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

Etapa 1

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

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Etapa 1.1

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

Etapa 1.2

Multiplique cada linha na primeira matriz por cada coluna na segunda matriz.

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

Etapa 1.3

Simplifique cada elemento da matriz multiplicando todas as expressões.

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

Etapa 2

Find the determinant.

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Etapa 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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Etapa 2.1.1

Consider the corresponding sign chart.

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

Etapa 2.1.2

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

Etapa 2.1.3

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

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

Etapa 2.1.4

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

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

Etapa 2.1.5

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

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

Etapa 2.1.6

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

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

Etapa 2.1.7

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

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

Etapa 2.1.8

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

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

Etapa 2.1.9

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

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

Etapa 2.1.10

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

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

Etapa 2.1.11

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

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

Etapa 2.1.12

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

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

Etapa 2.1.13

Add the terms together.

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

Etapa 2.2

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

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Etapa 2.2.1

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

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Etapa 2.2.1.1

Consider the corresponding sign chart.

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

Etapa 2.2.1.2

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

Etapa 2.2.1.3

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

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

Etapa 2.2.1.4

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

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

Etapa 2.2.1.5

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

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

Etapa 2.2.1.6

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

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

Etapa 2.2.1.7

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

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

Etapa 2.2.1.8

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

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

Etapa 2.2.1.9

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

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

Etapa 2.2.1.10

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

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

Etapa 2.2.1.11

Add the terms together.

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

Etapa 2.2.2

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

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Etapa 2.2.2.1

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

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Etapa 2.2.2.1.1

Consider the corresponding sign chart.

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

Etapa 2.2.2.1.2

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

Etapa 2.2.2.1.3

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

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

Etapa 2.2.2.1.4

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

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

Etapa 2.2.2.1.5

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

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

Etapa 2.2.2.1.6

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

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

Etapa 2.2.2.1.7

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

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

Etapa 2.2.2.1.8

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

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

Etapa 2.2.2.1.9

Add the terms together.

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

Etapa 2.2.2.2

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

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Etapa 2.2.2.2.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.2.2.2.2

Simplifique o determinante.

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Etapa 2.2.2.2.2.1

Simplifique cada termo.

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Etapa 2.2.2.2.2.1.1

Multiplique $82$ por $74$ .

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

Etapa 2.2.2.2.2.1.2

Multiplique $- 143$ por $106$ .

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

Etapa 2.2.2.2.2.2

Subtraia $15158$ de $6068$ .

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

Etapa 2.2.2.3

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

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Etapa 2.2.2.3.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.2.2.3.2

Simplifique o determinante.

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Etapa 2.2.2.3.2.1

Simplifique cada termo.

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Etapa 2.2.2.3.2.1.1

Multiplique $7$ por $74$ .

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

Etapa 2.2.2.3.2.1.2

Multiplique $- 175$ por $106$ .

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

Etapa 2.2.2.3.2.2

Subtraia $18550$ de $518$ .

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

Etapa 2.2.2.4

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

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Etapa 2.2.2.4.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.2.2.4.2

Simplifique o determinante.

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Etapa 2.2.2.4.2.1

Simplifique cada termo.

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Etapa 2.2.2.4.2.1.1

Multiplique $7$ por $143$ .

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

Etapa 2.2.2.4.2.1.2

Multiplique $- 175$ por $82$ .

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

Etapa 2.2.2.4.2.2

Subtraia $14350$ de $1001$ .

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

Etapa 2.2.2.5

Simplifique o determinante.

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Etapa 2.2.2.5.1

Simplifique cada termo.

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Etapa 2.2.2.5.1.1

Multiplique $239$ por $- 9090$ .

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

Etapa 2.2.2.5.1.2

Multiplique $- 218$ por $- 18032$ .

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

Etapa 2.2.2.5.1.3

Multiplique $- 55$ por $- 13349$ .

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

Etapa 2.2.2.5.2

Some $- 2172510$ e $3930976$ .

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

Etapa 2.2.2.5.3

Some $1758466$ e $734195$ .

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

Etapa 2.2.3

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

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Etapa 2.2.3.1

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

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Etapa 2.2.3.1.1

Consider the corresponding sign chart.

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

Etapa 2.2.3.1.2

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

Etapa 2.2.3.1.3

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

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

Etapa 2.2.3.1.4

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

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

Etapa 2.2.3.1.5

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

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

Etapa 2.2.3.1.6

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

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

Etapa 2.2.3.1.7

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

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

Etapa 2.2.3.1.8

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

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

Etapa 2.2.3.1.9

Add the terms together.

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

Etapa 2.2.3.2

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

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Etapa 2.2.3.2.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.2.3.2.2

Simplifique o determinante.

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Etapa 2.2.3.2.2.1

Simplifique cada termo.

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Etapa 2.2.3.2.2.1.1

Multiplique $82$ por $74$ .

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

Etapa 2.2.3.2.2.1.2

Multiplique $- 143$ por $106$ .

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

Etapa 2.2.3.2.2.2

Subtraia $15158$ de $6068$ .

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

Etapa 2.2.3.3

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

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Etapa 2.2.3.3.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.2.3.3.2

Simplifique o determinante.

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Etapa 2.2.3.3.2.1

Simplifique cada termo.

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Etapa 2.2.3.3.2.1.1

Multiplique $83$ por $74$ .

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

Etapa 2.2.3.3.2.1.2

Multiplique $- 20$ por $106$ .

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

Etapa 2.2.3.3.2.2

Subtraia $2120$ de $6142$ .

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

Etapa 2.2.3.4

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

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Etapa 2.2.3.4.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.2.3.4.2

Simplifique o determinante.

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Etapa 2.2.3.4.2.1

Simplifique cada termo.

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Etapa 2.2.3.4.2.1.1

Multiplique $83$ por $143$ .

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

Etapa 2.2.3.4.2.1.2

Multiplique $- 20$ por $82$ .

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

Etapa 2.2.3.4.2.2

Subtraia $1640$ de $11869$ .

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

Etapa 2.2.3.5

Simplifique o determinante.

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Etapa 2.2.3.5.1

Simplifique cada termo.

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Etapa 2.2.3.5.1.1

Multiplique $- 82$ por $- 9090$ .

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

Etapa 2.2.3.5.1.2

Multiplique $- 218$ por $4022$ .

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

Etapa 2.2.3.5.1.3

Multiplique $- 55$ por $10229$ .

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

Etapa 2.2.3.5.2

Subtraia $876796$ de $745380$ .

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

Etapa 2.2.3.5.3

Subtraia $562595$ de $- 131416$ .

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

Etapa 2.2.4

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

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Etapa 2.2.4.1

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

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Etapa 2.2.4.1.1

Consider the corresponding sign chart.

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

Etapa 2.2.4.1.2

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

Etapa 2.2.4.1.3

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

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

Etapa 2.2.4.1.4

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

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

Etapa 2.2.4.1.5

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

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

Etapa 2.2.4.1.6

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

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

Etapa 2.2.4.1.7

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

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

Etapa 2.2.4.1.8

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

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

Etapa 2.2.4.1.9

Add the terms together.

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

Etapa 2.2.4.2

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

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Etapa 2.2.4.2.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.2.4.2.2

Simplifique o determinante.

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Etapa 2.2.4.2.2.1

Simplifique cada termo.

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Etapa 2.2.4.2.2.1.1

Multiplique $7$ por $74$ .

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

Etapa 2.2.4.2.2.1.2

Multiplique $- 175$ por $106$ .

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

Etapa 2.2.4.2.2.2

Subtraia $18550$ de $518$ .

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

Etapa 2.2.4.3

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

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Etapa 2.2.4.3.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.2.4.3.2

Simplifique o determinante.

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Etapa 2.2.4.3.2.1

Simplifique cada termo.

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Etapa 2.2.4.3.2.1.1

Multiplique $83$ por $74$ .

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

Etapa 2.2.4.3.2.1.2

Multiplique $- 20$ por $106$ .

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

Etapa 2.2.4.3.2.2

Subtraia $2120$ de $6142$ .

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

Etapa 2.2.4.4

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

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Etapa 2.2.4.4.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.2.4.4.2

Simplifique o determinante.

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Etapa 2.2.4.4.2.1

Simplifique cada termo.

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Etapa 2.2.4.4.2.1.1

Multiplique $83$ por $175$ .

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

Etapa 2.2.4.4.2.1.2

Multiplique $- 20$ por $7$ .

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

Etapa 2.2.4.4.2.2

Subtraia $140$ de $14525$ .

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

Etapa 2.2.4.5

Simplifique o determinante.

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Etapa 2.2.4.5.1

Simplifique cada termo.

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Etapa 2.2.4.5.1.1

Multiplique $- 82$ por $- 18032$ .

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

Etapa 2.2.4.5.1.2

Multiplique $- 239$ por $4022$ .

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

Etapa 2.2.4.5.1.3

Multiplique $- 55$ por $14385$ .

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

Etapa 2.2.4.5.2

Subtraia $961258$ de $1478624$ .

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

Etapa 2.2.4.5.3

Subtraia $791175$ de $517366$ .

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

Etapa 2.2.5

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

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Etapa 2.2.5.1

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

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Etapa 2.2.5.1.1

Consider the corresponding sign chart.

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

Etapa 2.2.5.1.2

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

Etapa 2.2.5.1.3

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

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

Etapa 2.2.5.1.4

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

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

Etapa 2.2.5.1.5

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

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

Etapa 2.2.5.1.6

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

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

Etapa 2.2.5.1.7

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

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

Etapa 2.2.5.1.8

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

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

Etapa 2.2.5.1.9

Add the terms together.

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

Etapa 2.2.5.2

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

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Etapa 2.2.5.2.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.2.5.2.2

Simplifique o determinante.

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Etapa 2.2.5.2.2.1

Simplifique cada termo.

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Etapa 2.2.5.2.2.1.1

Multiplique $7$ por $143$ .

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

Etapa 2.2.5.2.2.1.2

Multiplique $- 175$ por $82$ .

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

Etapa 2.2.5.2.2.2

Subtraia $14350$ de $1001$ .

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

Etapa 2.2.5.3

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

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Etapa 2.2.5.3.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.2.5.3.2

Simplifique o determinante.

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Etapa 2.2.5.3.2.1

Simplifique cada termo.

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Etapa 2.2.5.3.2.1.1

Multiplique $83$ por $143$ .

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

Etapa 2.2.5.3.2.1.2

Multiplique $- 20$ por $82$ .

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

Etapa 2.2.5.3.2.2

Subtraia $1640$ de $11869$ .

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

Etapa 2.2.5.4

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

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Etapa 2.2.5.4.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.2.5.4.2

Simplifique o determinante.

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Etapa 2.2.5.4.2.1

Simplifique cada termo.

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Etapa 2.2.5.4.2.1.1

Multiplique $83$ por $175$ .

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

Etapa 2.2.5.4.2.1.2

Multiplique $- 20$ por $7$ .

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

Etapa 2.2.5.4.2.2

Subtraia $140$ de $14525$ .

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

Etapa 2.2.5.5

Simplifique o determinante.

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Etapa 2.2.5.5.1

Simplifique cada termo.

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Etapa 2.2.5.5.1.1

Multiplique $- 82$ por $- 13349$ .

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

Etapa 2.2.5.5.1.2

Multiplique $- 239$ por $10229$ .

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

Etapa 2.2.5.5.1.3

Multiplique $218$ por $14385$ .

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

Etapa 2.2.5.5.2

Subtraia $2444731$ de $1094618$ .

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

Etapa 2.2.5.5.3

Some $- 1350113$ e $3135930$ .

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

Etapa 2.2.6

Simplifique o determinante.

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Etapa 2.2.6.1

Simplifique cada termo.

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Etapa 2.2.6.1.1

Multiplique $169$ por $2492661$ .

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

Etapa 2.2.6.1.2

Multiplique $164$ por $- 694011$ .

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

Etapa 2.2.6.1.3

Multiplique $18$ por $- 273809$ .

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

Etapa 2.2.6.1.4

Multiplique $- 105$ por $1785817$ .

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

Etapa 2.2.6.2

Subtraia $113817804$ de $421259709$ .

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

Etapa 2.2.6.3

Subtraia $4928562$ de $307441905$ .

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

Etapa 2.2.6.4

Subtraia $187510785$ de $302513343$ .

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

Etapa 2.3

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

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Etapa 2.3.1

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

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Etapa 2.3.1.1

Consider the corresponding sign chart.

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

Etapa 2.3.1.2

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

Etapa 2.3.1.3

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

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

Etapa 2.3.1.4

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

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

Etapa 2.3.1.5

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

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

Etapa 2.3.1.6

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

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

Etapa 2.3.1.7

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

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

Etapa 2.3.1.8

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

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

Etapa 2.3.1.9

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

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

Etapa 2.3.1.10

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

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

Etapa 2.3.1.11

Add the terms together.

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

Etapa 2.3.2

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

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Etapa 2.3.2.1

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

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Etapa 2.3.2.1.1

Consider the corresponding sign chart.

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

Etapa 2.3.2.1.2

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

Etapa 2.3.2.1.3

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

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

Etapa 2.3.2.1.4

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

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

Etapa 2.3.2.1.5

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

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

Etapa 2.3.2.1.6

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

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

Etapa 2.3.2.1.7

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

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

Etapa 2.3.2.1.8

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

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

Etapa 2.3.2.1.9

Add the terms together.

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

Etapa 2.3.2.2

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

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Etapa 2.3.2.2.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.3.2.2.2

Simplifique o determinante.

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Etapa 2.3.2.2.2.1

Simplifique cada termo.

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Etapa 2.3.2.2.2.1.1

Multiplique $82$ por $74$ .

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

Etapa 2.3.2.2.2.1.2

Multiplique $- 143$ por $106$ .

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

Etapa 2.3.2.2.2.2

Subtraia $15158$ de $6068$ .

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

Etapa 2.3.2.3

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

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Etapa 2.3.2.3.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.3.2.3.2

Simplifique o determinante.

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Etapa 2.3.2.3.2.1

Simplifique cada termo.

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Etapa 2.3.2.3.2.1.1

Multiplique $7$ por $74$ .

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

Etapa 2.3.2.3.2.1.2

Multiplique $- 175$ por $106$ .

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

Etapa 2.3.2.3.2.2

Subtraia $18550$ de $518$ .

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

Etapa 2.3.2.4

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

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Etapa 2.3.2.4.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.3.2.4.2

Simplifique o determinante.

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Etapa 2.3.2.4.2.1

Simplifique cada termo.

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Etapa 2.3.2.4.2.1.1

Multiplique $7$ por $143$ .

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

Etapa 2.3.2.4.2.1.2

Multiplique $- 175$ por $82$ .

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

Etapa 2.3.2.4.2.2

Subtraia $14350$ de $1001$ .

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

Etapa 2.3.2.5

Simplifique o determinante.

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Etapa 2.3.2.5.1

Simplifique cada termo.

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Etapa 2.3.2.5.1.1

Multiplique $239$ por $- 9090$ .

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

Etapa 2.3.2.5.1.2

Multiplique $- 218$ por $- 18032$ .

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

Etapa 2.3.2.5.1.3

Multiplique $- 55$ por $- 13349$ .

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

Etapa 2.3.2.5.2

Some $- 2172510$ e $3930976$ .

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

Etapa 2.3.2.5.3

Some $1758466$ e $734195$ .

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

Etapa 2.3.3

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

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Etapa 2.3.3.1

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

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Etapa 2.3.3.1.1

Consider the corresponding sign chart.

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

Etapa 2.3.3.1.2

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

Etapa 2.3.3.1.3

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

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

Etapa 2.3.3.1.4

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

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

Etapa 2.3.3.1.5

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

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

Etapa 2.3.3.1.6

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

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

Etapa 2.3.3.1.7

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

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

Etapa 2.3.3.1.8

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

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

Etapa 2.3.3.1.9

Add the terms together.

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

Etapa 2.3.3.2

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

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Etapa 2.3.3.2.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.3.3.2.2

Simplifique o determinante.

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Etapa 2.3.3.2.2.1

Simplifique cada termo.

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Etapa 2.3.3.2.2.1.1

Multiplique $82$ por $74$ .

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

Etapa 2.3.3.2.2.1.2

Multiplique $- 143$ por $106$ .

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

Etapa 2.3.3.2.2.2

Subtraia $15158$ de $6068$ .

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

Etapa 2.3.3.3

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

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Etapa 2.3.3.3.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.3.3.3.2

Simplifique o determinante.

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Etapa 2.3.3.3.2.1

Simplifique cada termo.

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Etapa 2.3.3.3.2.1.1

Multiplique $119$ por $74$ .

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

Etapa 2.3.3.3.2.1.2

Multiplique $- 162$ por $106$ .

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

Etapa 2.3.3.3.2.2

Subtraia $17172$ de $8806$ .

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

Etapa 2.3.3.4

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

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Etapa 2.3.3.4.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.3.3.4.2

Simplifique o determinante.

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Etapa 2.3.3.4.2.1

Simplifique cada termo.

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Etapa 2.3.3.4.2.1.1

Multiplique $119$ por $143$ .

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

Etapa 2.3.3.4.2.1.2

Multiplique $- 162$ por $82$ .

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

Etapa 2.3.3.4.2.2

Subtraia $13284$ de $17017$ .

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

Etapa 2.3.3.5

Simplifique o determinante.

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Etapa 2.3.3.5.1

Simplifique cada termo.

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Etapa 2.3.3.5.1.1

Multiplique $113$ por $- 9090$ .

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

Etapa 2.3.3.5.1.2

Multiplique $- 218$ por $- 8366$ .

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

Etapa 2.3.3.5.1.3

Multiplique $- 55$ por $3733$ .

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

Etapa 2.3.3.5.2

Some $- 1027170$ e $1823788$ .

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

Etapa 2.3.3.5.3

Subtraia $205315$ de $796618$ .

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

Etapa 2.3.4

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

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Etapa 2.3.4.1

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

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Etapa 2.3.4.1.1

Consider the corresponding sign chart.

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

Etapa 2.3.4.1.2

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

Etapa 2.3.4.1.3

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

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

Etapa 2.3.4.1.4

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

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

Etapa 2.3.4.1.5

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

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

Etapa 2.3.4.1.6

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

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

Etapa 2.3.4.1.7

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

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

Etapa 2.3.4.1.8

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

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

Etapa 2.3.4.1.9

Add the terms together.

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

Etapa 2.3.4.2

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

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Etapa 2.3.4.2.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.3.4.2.2

Simplifique o determinante.

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Etapa 2.3.4.2.2.1

Simplifique cada termo.

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Etapa 2.3.4.2.2.1.1

Multiplique $7$ por $74$ .

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

Etapa 2.3.4.2.2.1.2

Multiplique $- 175$ por $106$ .

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

Etapa 2.3.4.2.2.2

Subtraia $18550$ de $518$ .

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

Etapa 2.3.4.3

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

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Etapa 2.3.4.3.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.3.4.3.2

Simplifique o determinante.

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Etapa 2.3.4.3.2.1

Simplifique cada termo.

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Etapa 2.3.4.3.2.1.1

Multiplique $119$ por $74$ .

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

Etapa 2.3.4.3.2.1.2

Multiplique $- 162$ por $106$ .

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

Etapa 2.3.4.3.2.2

Subtraia $17172$ de $8806$ .

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

Etapa 2.3.4.4

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

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Etapa 2.3.4.4.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.3.4.4.2

Simplifique o determinante.

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Etapa 2.3.4.4.2.1

Simplifique cada termo.

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Etapa 2.3.4.4.2.1.1

Multiplique $119$ por $175$ .

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

Etapa 2.3.4.4.2.1.2

Multiplique $- 162$ por $7$ .

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

Etapa 2.3.4.4.2.2

Subtraia $1134$ de $20825$ .

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

Etapa 2.3.4.5

Simplifique o determinante.

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Etapa 2.3.4.5.1

Simplifique cada termo.

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Etapa 2.3.4.5.1.1

Multiplique $113$ por $- 18032$ .

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

Etapa 2.3.4.5.1.2

Multiplique $- 239$ por $- 8366$ .

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

Etapa 2.3.4.5.1.3

Multiplique $- 55$ por $19691$ .

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

Etapa 2.3.4.5.2

Some $- 2037616$ e $1999474$ .

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

Etapa 2.3.4.5.3

Subtraia $1083005$ de $- 38142$ .

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

Etapa 2.3.5

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

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Etapa 2.3.5.1

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

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Etapa 2.3.5.1.1

Consider the corresponding sign chart.

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

Etapa 2.3.5.1.2

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

Etapa 2.3.5.1.3

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

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

Etapa 2.3.5.1.4

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

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

Etapa 2.3.5.1.5

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

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

Etapa 2.3.5.1.6

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

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

Etapa 2.3.5.1.7

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

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

Etapa 2.3.5.1.8

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

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

Etapa 2.3.5.1.9

Add the terms together.

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

Etapa 2.3.5.2

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

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Etapa 2.3.5.2.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.3.5.2.2

Simplifique o determinante.

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Etapa 2.3.5.2.2.1

Simplifique cada termo.

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Etapa 2.3.5.2.2.1.1

Multiplique $7$ por $143$ .

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

Etapa 2.3.5.2.2.1.2

Multiplique $- 175$ por $82$ .

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

Etapa 2.3.5.2.2.2

Subtraia $14350$ de $1001$ .

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

Etapa 2.3.5.3

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

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Etapa 2.3.5.3.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.3.5.3.2

Simplifique o determinante.

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Etapa 2.3.5.3.2.1

Simplifique cada termo.

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Etapa 2.3.5.3.2.1.1

Multiplique $119$ por $143$ .

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

Etapa 2.3.5.3.2.1.2

Multiplique $- 162$ por $82$ .

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

Etapa 2.3.5.3.2.2

Subtraia $13284$ de $17017$ .

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

Etapa 2.3.5.4

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

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Etapa 2.3.5.4.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.3.5.4.2

Simplifique o determinante.

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Etapa 2.3.5.4.2.1

Simplifique cada termo.

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Etapa 2.3.5.4.2.1.1

Multiplique $119$ por $175$ .

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

Etapa 2.3.5.4.2.1.2

Multiplique $- 162$ por $7$ .

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

Etapa 2.3.5.4.2.2

Subtraia $1134$ de $20825$ .

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

Etapa 2.3.5.5

Simplifique o determinante.

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Etapa 2.3.5.5.1

Simplifique cada termo.

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Etapa 2.3.5.5.1.1

Multiplique $113$ por $- 13349$ .

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

Etapa 2.3.5.5.1.2

Multiplique $- 239$ por $3733$ .

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

Etapa 2.3.5.5.1.3

Multiplique $218$ por $19691$ .

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

Etapa 2.3.5.5.2

Subtraia $892187$ de $- 1508437$ .

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

Etapa 2.3.5.5.3

Some $- 2400624$ e $4292638$ .

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

Etapa 2.3.6

Simplifique o determinante.

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Etapa 2.3.6.1

Simplifique cada termo.

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Etapa 2.3.6.1.1

Multiplique $20$ por $2492661$ .

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

Etapa 2.3.6.1.2

Multiplique $164$ por $591303$ .

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

Etapa 2.3.6.1.3

Multiplique $18$ por $- 1121147$ .

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

Etapa 2.3.6.1.4

Multiplique $- 105$ por $1892014$ .

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

Etapa 2.3.6.2

Some $49853220$ e $96973692$ .

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

Etapa 2.3.6.3

Subtraia $20180646$ de $146826912$ .

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

Etapa 2.3.6.4

Subtraia $198661470$ de $126646266$ .

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

Etapa 2.4

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

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Etapa 2.4.1

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

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Etapa 2.4.1.1

Consider the corresponding sign chart.

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

Etapa 2.4.1.2

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

Etapa 2.4.1.3

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

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

Etapa 2.4.1.4

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

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

Etapa 2.4.1.5

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

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

Etapa 2.4.1.6

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

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

Etapa 2.4.1.7

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

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

Etapa 2.4.1.8

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

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

Etapa 2.4.1.9

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

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

Etapa 2.4.1.10

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

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

Etapa 2.4.1.11

Add the terms together.

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

Etapa 2.4.2

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

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Etapa 2.4.2.1

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

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Etapa 2.4.2.1.1

Consider the corresponding sign chart.

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

Etapa 2.4.2.1.2

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

Etapa 2.4.2.1.3

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

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

Etapa 2.4.2.1.4

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

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

Etapa 2.4.2.1.5

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

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

Etapa 2.4.2.1.6

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

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

Etapa 2.4.2.1.7

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

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

Etapa 2.4.2.1.8

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

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

Etapa 2.4.2.1.9

Add the terms together.

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

Etapa 2.4.2.2

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

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Etapa 2.4.2.2.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.4.2.2.2

Simplifique o determinante.

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Etapa 2.4.2.2.2.1

Simplifique cada termo.

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Etapa 2.4.2.2.2.1.1

Multiplique $82$ por $74$ .

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

Etapa 2.4.2.2.2.1.2

Multiplique $- 143$ por $106$ .

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

Etapa 2.4.2.2.2.2

Subtraia $15158$ de $6068$ .

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

Etapa 2.4.2.3

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

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Etapa 2.4.2.3.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.4.2.3.2

Simplifique o determinante.

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Etapa 2.4.2.3.2.1

Simplifique cada termo.

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Etapa 2.4.2.3.2.1.1

Multiplique $83$ por $74$ .

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

Etapa 2.4.2.3.2.1.2

Multiplique $- 20$ por $106$ .

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

Etapa 2.4.2.3.2.2

Subtraia $2120$ de $6142$ .

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

Etapa 2.4.2.4

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

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Etapa 2.4.2.4.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.4.2.4.2

Simplifique o determinante.

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Etapa 2.4.2.4.2.1

Simplifique cada termo.

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Etapa 2.4.2.4.2.1.1

Multiplique $83$ por $143$ .

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

Etapa 2.4.2.4.2.1.2

Multiplique $- 20$ por $82$ .

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

Etapa 2.4.2.4.2.2

Subtraia $1640$ de $11869$ .

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

Etapa 2.4.2.5

Simplifique o determinante.

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Etapa 2.4.2.5.1

Simplifique cada termo.

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Etapa 2.4.2.5.1.1

Multiplique $- 82$ por $- 9090$ .

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

Etapa 2.4.2.5.1.2

Multiplique $- 218$ por $4022$ .

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

Etapa 2.4.2.5.1.3

Multiplique $- 55$ por $10229$ .

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

Etapa 2.4.2.5.2

Subtraia $876796$ de $745380$ .

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

Etapa 2.4.2.5.3

Subtraia $562595$ de $- 131416$ .

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

Etapa 2.4.3

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

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Etapa 2.4.3.1

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

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Etapa 2.4.3.1.1

Consider the corresponding sign chart.

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

Etapa 2.4.3.1.2

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

Etapa 2.4.3.1.3

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

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

Etapa 2.4.3.1.4

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

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

Etapa 2.4.3.1.5

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

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

Etapa 2.4.3.1.6

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

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

Etapa 2.4.3.1.7

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

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

Etapa 2.4.3.1.8

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

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

Etapa 2.4.3.1.9

Add the terms together.

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

Etapa 2.4.3.2

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

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Etapa 2.4.3.2.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.4.3.2.2

Simplifique o determinante.

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Etapa 2.4.3.2.2.1

Simplifique cada termo.

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Etapa 2.4.3.2.2.1.1

Multiplique $82$ por $74$ .

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

Etapa 2.4.3.2.2.1.2

Multiplique $- 143$ por $106$ .

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

Etapa 2.4.3.2.2.2

Subtraia $15158$ de $6068$ .

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

Etapa 2.4.3.3

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

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Etapa 2.4.3.3.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.4.3.3.2

Simplifique o determinante.

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Etapa 2.4.3.3.2.1

Simplifique cada termo.

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Etapa 2.4.3.3.2.1.1

Multiplique $119$ por $74$ .

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

Etapa 2.4.3.3.2.1.2

Multiplique $- 162$ por $106$ .

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

Etapa 2.4.3.3.2.2

Subtraia $17172$ de $8806$ .

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

Etapa 2.4.3.4

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

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Etapa 2.4.3.4.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.4.3.4.2

Simplifique o determinante.

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Etapa 2.4.3.4.2.1

Simplifique cada termo.

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Etapa 2.4.3.4.2.1.1

Multiplique $119$ por $143$ .

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

Etapa 2.4.3.4.2.1.2

Multiplique $- 162$ por $82$ .

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

Etapa 2.4.3.4.2.2

Subtraia $13284$ de $17017$ .

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

Etapa 2.4.3.5

Simplifique o determinante.

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Etapa 2.4.3.5.1

Simplifique cada termo.

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Etapa 2.4.3.5.1.1

Multiplique $113$ por $- 9090$ .

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

Etapa 2.4.3.5.1.2

Multiplique $- 218$ por $- 8366$ .

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

Etapa 2.4.3.5.1.3

Multiplique $- 55$ por $3733$ .

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

Etapa 2.4.3.5.2

Some $- 1027170$ e $1823788$ .

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

Etapa 2.4.3.5.3

Subtraia $205315$ de $796618$ .

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

Etapa 2.4.4

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

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Etapa 2.4.4.1

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

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Etapa 2.4.4.1.1

Consider the corresponding sign chart.

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

Etapa 2.4.4.1.2

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

Etapa 2.4.4.1.3

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

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

Etapa 2.4.4.1.4

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

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

Etapa 2.4.4.1.5

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

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

Etapa 2.4.4.1.6

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

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

Etapa 2.4.4.1.7

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

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

Etapa 2.4.4.1.8

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

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

Etapa 2.4.4.1.9

Add the terms together.

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

Etapa 2.4.4.2

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

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Etapa 2.4.4.2.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.4.4.2.2

Simplifique o determinante.

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Etapa 2.4.4.2.2.1

Simplifique cada termo.

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Etapa 2.4.4.2.2.1.1

Multiplique $83$ por $74$ .

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

Etapa 2.4.4.2.2.1.2

Multiplique $- 20$ por $106$ .

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

Etapa 2.4.4.2.2.2

Subtraia $2120$ de $6142$ .

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

Etapa 2.4.4.3

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

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Etapa 2.4.4.3.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.4.4.3.2

Simplifique o determinante.

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Etapa 2.4.4.3.2.1

Simplifique cada termo.

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Etapa 2.4.4.3.2.1.1

Multiplique $119$ por $74$ .

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

Etapa 2.4.4.3.2.1.2

Multiplique $- 162$ por $106$ .

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

Etapa 2.4.4.3.2.2

Subtraia $17172$ de $8806$ .

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

Etapa 2.4.4.4

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

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Etapa 2.4.4.4.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.4.4.4.2

Simplifique o determinante.

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Etapa 2.4.4.4.2.1

Simplifique cada termo.

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Etapa 2.4.4.4.2.1.1

Multiplique $119$ por $20$ .

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

Etapa 2.4.4.4.2.1.2

Multiplique $- 162$ por $83$ .

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

Etapa 2.4.4.4.2.2

Subtraia $13446$ de $2380$ .

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

Etapa 2.4.4.5

Simplifique o determinante.

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Etapa 2.4.4.5.1

Simplifique cada termo.

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Etapa 2.4.4.5.1.1

Multiplique $113$ por $4022$ .

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

Etapa 2.4.4.5.1.2

Multiplique $82$ por $- 8366$ .

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

Etapa 2.4.4.5.1.3

Multiplique $- 55$ por $- 11066$ .

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

Etapa 2.4.4.5.2

Subtraia $686012$ de $454486$ .

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

Etapa 2.4.4.5.3

Some $- 231526$ e $608630$ .

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

Etapa 2.4.5

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

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Etapa 2.4.5.1

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

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Etapa 2.4.5.1.1

Consider the corresponding sign chart.

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

Etapa 2.4.5.1.2

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

Etapa 2.4.5.1.3

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

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

Etapa 2.4.5.1.4

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

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

Etapa 2.4.5.1.5

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

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

Etapa 2.4.5.1.6

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

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

Etapa 2.4.5.1.7

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

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

Etapa 2.4.5.1.8

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

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

Etapa 2.4.5.1.9

Add the terms together.

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

Etapa 2.4.5.2

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

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Etapa 2.4.5.2.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.4.5.2.2

Simplifique o determinante.

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Etapa 2.4.5.2.2.1

Simplifique cada termo.

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Etapa 2.4.5.2.2.1.1

Multiplique $83$ por $143$ .

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

Etapa 2.4.5.2.2.1.2

Multiplique $- 20$ por $82$ .

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

Etapa 2.4.5.2.2.2

Subtraia $1640$ de $11869$ .

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

Etapa 2.4.5.3

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

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Etapa 2.4.5.3.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.4.5.3.2

Simplifique o determinante.

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Etapa 2.4.5.3.2.1

Simplifique cada termo.

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Etapa 2.4.5.3.2.1.1

Multiplique $119$ por $143$ .

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

Etapa 2.4.5.3.2.1.2

Multiplique $- 162$ por $82$ .

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

Etapa 2.4.5.3.2.2

Subtraia $13284$ de $17017$ .

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

Etapa 2.4.5.4

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

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Etapa 2.4.5.4.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.4.5.4.2

Simplifique o determinante.

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Etapa 2.4.5.4.2.1

Simplifique cada termo.

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Etapa 2.4.5.4.2.1.1

Multiplique $119$ por $20$ .

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

Etapa 2.4.5.4.2.1.2

Multiplique $- 162$ por $83$ .

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

Etapa 2.4.5.4.2.2

Subtraia $13446$ de $2380$ .

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

Etapa 2.4.5.5

Simplifique o determinante.

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Etapa 2.4.5.5.1

Simplifique cada termo.

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Etapa 2.4.5.5.1.1

Multiplique $113$ por $10229$ .

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

Etapa 2.4.5.5.1.2

Multiplique $82$ por $3733$ .

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

Etapa 2.4.5.5.1.3

Multiplique $218$ por $- 11066$ .

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

Etapa 2.4.5.5.2

Some $1155877$ e $306106$ .

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

Etapa 2.4.5.5.3

Subtraia $2412388$ de $1461983$ .

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

Etapa 2.4.6

Simplifique o determinante.

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Etapa 2.4.6.1

Simplifique cada termo.

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Etapa 2.4.6.1.1

Multiplique $20$ por $- 694011$ .

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

Etapa 2.4.6.1.2

Multiplique $- 169$ por $591303$ .

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

Etapa 2.4.6.1.3

Multiplique $18$ por $377104$ .

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

Etapa 2.4.6.1.4

Multiplique $- 105$ por $- 950405$ .

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

Etapa 2.4.6.2

Subtraia $99930207$ de $- 13880220$ .

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

Etapa 2.4.6.3

Some $- 113810427$ e $6787872$ .

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

Etapa 2.4.6.4

Some $- 107022555$ e $99792525$ .

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

Etapa 2.5

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

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Etapa 2.5.1

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

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Etapa 2.5.1.1

Consider the corresponding sign chart.

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

Etapa 2.5.1.2

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

Etapa 2.5.1.3

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

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

Etapa 2.5.1.4

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

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

Etapa 2.5.1.5

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

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

Etapa 2.5.1.6

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

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

Etapa 2.5.1.7

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

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

Etapa 2.5.1.8

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

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

Etapa 2.5.1.9

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

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

Etapa 2.5.1.10

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

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

Etapa 2.5.1.11

Add the terms together.

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

Etapa 2.5.2

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

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Etapa 2.5.2.1

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

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Etapa 2.5.2.1.1

Consider the corresponding sign chart.

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

Etapa 2.5.2.1.2

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

Etapa 2.5.2.1.3

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

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

Etapa 2.5.2.1.4

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

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

Etapa 2.5.2.1.5

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

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

Etapa 2.5.2.1.6

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

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

Etapa 2.5.2.1.7

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

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

Etapa 2.5.2.1.8

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

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

Etapa 2.5.2.1.9

Add the terms together.

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

Etapa 2.5.2.2

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

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Etapa 2.5.2.2.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.5.2.2.2

Simplifique o determinante.

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Etapa 2.5.2.2.2.1

Simplifique cada termo.

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Etapa 2.5.2.2.2.1.1

Multiplique $7$ por $74$ .

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

Etapa 2.5.2.2.2.1.2

Multiplique $- 175$ por $106$ .

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

Etapa 2.5.2.2.2.2

Subtraia $18550$ de $518$ .

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

Etapa 2.5.2.3

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

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Etapa 2.5.2.3.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.5.2.3.2

Simplifique o determinante.

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Etapa 2.5.2.3.2.1

Simplifique cada termo.

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Etapa 2.5.2.3.2.1.1

Multiplique $83$ por $74$ .

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

Etapa 2.5.2.3.2.1.2

Multiplique $- 20$ por $106$ .

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

Etapa 2.5.2.3.2.2

Subtraia $2120$ de $6142$ .

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

Etapa 2.5.2.4

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

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Etapa 2.5.2.4.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.5.2.4.2

Simplifique o determinante.

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Etapa 2.5.2.4.2.1

Simplifique cada termo.

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Etapa 2.5.2.4.2.1.1

Multiplique $83$ por $175$ .

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

Etapa 2.5.2.4.2.1.2

Multiplique $- 20$ por $7$ .

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

Etapa 2.5.2.4.2.2

Subtraia $140$ de $14525$ .

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

Etapa 2.5.2.5

Simplifique o determinante.

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Etapa 2.5.2.5.1

Simplifique cada termo.

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Etapa 2.5.2.5.1.1

Multiplique $- 82$ por $- 18032$ .

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

Etapa 2.5.2.5.1.2

Multiplique $- 239$ por $4022$ .

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

Etapa 2.5.2.5.1.3

Multiplique $- 55$ por $14385$ .

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

Etapa 2.5.2.5.2

Subtraia $961258$ de $1478624$ .

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

Etapa 2.5.2.5.3

Subtraia $791175$ de $517366$ .

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

Etapa 2.5.3

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

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Etapa 2.5.3.1

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

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Etapa 2.5.3.1.1

Consider the corresponding sign chart.

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

Etapa 2.5.3.1.2

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

Etapa 2.5.3.1.3

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

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

Etapa 2.5.3.1.4

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

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

Etapa 2.5.3.1.5

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

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

Etapa 2.5.3.1.6

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

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

Etapa 2.5.3.1.7

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

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

Etapa 2.5.3.1.8

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

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

Etapa 2.5.3.1.9

Add the terms together.

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

Etapa 2.5.3.2

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

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Etapa 2.5.3.2.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.5.3.2.2

Simplifique o determinante.

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Etapa 2.5.3.2.2.1

Simplifique cada termo.

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Etapa 2.5.3.2.2.1.1

Multiplique $7$ por $74$ .

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

Etapa 2.5.3.2.2.1.2

Multiplique $- 175$ por $106$ .

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

Etapa 2.5.3.2.2.2

Subtraia $18550$ de $518$ .

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

Etapa 2.5.3.3

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

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Etapa 2.5.3.3.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.5.3.3.2

Simplifique o determinante.

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Etapa 2.5.3.3.2.1

Simplifique cada termo.

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Etapa 2.5.3.3.2.1.1

Multiplique $119$ por $74$ .

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

Etapa 2.5.3.3.2.1.2

Multiplique $- 162$ por $106$ .

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

Etapa 2.5.3.3.2.2

Subtraia $17172$ de $8806$ .

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

Etapa 2.5.3.4

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

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Etapa 2.5.3.4.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.5.3.4.2

Simplifique o determinante.

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Etapa 2.5.3.4.2.1

Simplifique cada termo.

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Etapa 2.5.3.4.2.1.1

Multiplique $119$ por $175$ .

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

Etapa 2.5.3.4.2.1.2

Multiplique $- 162$ por $7$ .

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

Etapa 2.5.3.4.2.2

Subtraia $1134$ de $20825$ .

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

Etapa 2.5.3.5

Simplifique o determinante.

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Etapa 2.5.3.5.1

Simplifique cada termo.

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Etapa 2.5.3.5.1.1

Multiplique $113$ por $- 18032$ .

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

Etapa 2.5.3.5.1.2

Multiplique $- 239$ por $- 8366$ .

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

Etapa 2.5.3.5.1.3

Multiplique $- 55$ por $19691$ .

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

Etapa 2.5.3.5.2

Some $- 2037616$ e $1999474$ .

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

Etapa 2.5.3.5.3

Subtraia $1083005$ de $- 38142$ .

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

Etapa 2.5.4

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

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Etapa 2.5.4.1

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

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Etapa 2.5.4.1.1

Consider the corresponding sign chart.

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

Etapa 2.5.4.1.2

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

Etapa 2.5.4.1.3

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

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

Etapa 2.5.4.1.4

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

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

Etapa 2.5.4.1.5

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

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

Etapa 2.5.4.1.6

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

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

Etapa 2.5.4.1.7

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

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

Etapa 2.5.4.1.8

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

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

Etapa 2.5.4.1.9

Add the terms together.

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

Etapa 2.5.4.2

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

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Etapa 2.5.4.2.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.5.4.2.2

Simplifique o determinante.

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Etapa 2.5.4.2.2.1

Simplifique cada termo.

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Etapa 2.5.4.2.2.1.1

Multiplique $83$ por $74$ .

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

Etapa 2.5.4.2.2.1.2

Multiplique $- 20$ por $106$ .

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

Etapa 2.5.4.2.2.2

Subtraia $2120$ de $6142$ .

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

Etapa 2.5.4.3

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

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Etapa 2.5.4.3.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.5.4.3.2

Simplifique o determinante.

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Etapa 2.5.4.3.2.1

Simplifique cada termo.

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Etapa 2.5.4.3.2.1.1

Multiplique $119$ por $74$ .

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

Etapa 2.5.4.3.2.1.2

Multiplique $- 162$ por $106$ .

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

Etapa 2.5.4.3.2.2

Subtraia $17172$ de $8806$ .

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

Etapa 2.5.4.4

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

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Etapa 2.5.4.4.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.5.4.4.2

Simplifique o determinante.

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Etapa 2.5.4.4.2.1

Simplifique cada termo.

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Etapa 2.5.4.4.2.1.1

Multiplique $119$ por $20$ .

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

Etapa 2.5.4.4.2.1.2

Multiplique $- 162$ por $83$ .

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

Etapa 2.5.4.4.2.2

Subtraia $13446$ de $2380$ .

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

Etapa 2.5.4.5

Simplifique o determinante.

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Etapa 2.5.4.5.1

Simplifique cada termo.

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Etapa 2.5.4.5.1.1

Multiplique $113$ por $4022$ .

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

Etapa 2.5.4.5.1.2

Multiplique $82$ por $- 8366$ .

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

Etapa 2.5.4.5.1.3

Multiplique $- 55$ por $- 11066$ .

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

Etapa 2.5.4.5.2

Subtraia $686012$ de $454486$ .

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

Etapa 2.5.4.5.3

Some $- 231526$ e $608630$ .

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

Etapa 2.5.5

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

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Etapa 2.5.5.1

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

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Etapa 2.5.5.1.1

Consider the corresponding sign chart.

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

Etapa 2.5.5.1.2

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

Etapa 2.5.5.1.3

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

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

Etapa 2.5.5.1.4

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

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

Etapa 2.5.5.1.5

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

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

Etapa 2.5.5.1.6

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

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

Etapa 2.5.5.1.7

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

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

Etapa 2.5.5.1.8

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

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

Etapa 2.5.5.1.9

Add the terms together.

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

Etapa 2.5.5.2

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

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Etapa 2.5.5.2.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.5.5.2.2

Simplifique o determinante.

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Etapa 2.5.5.2.2.1

Simplifique cada termo.

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Etapa 2.5.5.2.2.1.1

Multiplique $83$ por $175$ .

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

Etapa 2.5.5.2.2.1.2

Multiplique $- 20$ por $7$ .

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

Etapa 2.5.5.2.2.2

Subtraia $140$ de $14525$ .

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

Etapa 2.5.5.3

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

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Etapa 2.5.5.3.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.5.5.3.2

Simplifique o determinante.

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Etapa 2.5.5.3.2.1

Simplifique cada termo.

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Etapa 2.5.5.3.2.1.1

Multiplique $119$ por $175$ .

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

Etapa 2.5.5.3.2.1.2

Multiplique $- 162$ por $7$ .

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

Etapa 2.5.5.3.2.2

Subtraia $1134$ de $20825$ .

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

Etapa 2.5.5.4

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

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Etapa 2.5.5.4.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.5.5.4.2

Simplifique o determinante.

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Etapa 2.5.5.4.2.1

Simplifique cada termo.

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Etapa 2.5.5.4.2.1.1

Multiplique $119$ por $20$ .

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

Etapa 2.5.5.4.2.1.2

Multiplique $- 162$ por $83$ .

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

Etapa 2.5.5.4.2.2

Subtraia $13446$ de $2380$ .

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

Etapa 2.5.5.5

Simplifique o determinante.

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Etapa 2.5.5.5.1

Simplifique cada termo.

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Etapa 2.5.5.5.1.1

Multiplique $113$ por $14385$ .

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

Etapa 2.5.5.5.1.2

Multiplique $82$ por $19691$ .

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

Etapa 2.5.5.5.1.3

Multiplique $239$ por $- 11066$ .

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

Etapa 2.5.5.5.2

Some $1625505$ e $1614662$ .

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

Etapa 2.5.5.5.3

Subtraia $2644774$ de $3240167$ .

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

Etapa 2.5.6

Simplifique o determinante.

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Etapa 2.5.6.1

Simplifique cada termo.

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Etapa 2.5.6.1.1

Multiplique $20$ por $- 273809$ .

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

Etapa 2.5.6.1.2

Multiplique $- 169$ por $- 1121147$ .

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

Etapa 2.5.6.1.3

Multiplique $- 164$ por $377104$ .

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

Etapa 2.5.6.1.4

Multiplique $- 105$ por $595393$ .

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

Etapa 2.5.6.2

Some $- 5476180$ e $189473843$ .

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

Etapa 2.5.6.3

Subtraia $61845056$ de $183997663$ .

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

Etapa 2.5.6.4

Subtraia $62516265$ de $122152607$ .

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

Etapa 2.6

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

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Etapa 2.6.1

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

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Etapa 2.6.1.1

Consider the corresponding sign chart.

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

Etapa 2.6.1.2

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

Etapa 2.6.1.3

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

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

Etapa 2.6.1.4

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

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

Etapa 2.6.1.5

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

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

Etapa 2.6.1.6

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

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

Etapa 2.6.1.7

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

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

Etapa 2.6.1.8

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

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

Etapa 2.6.1.9

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

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

Etapa 2.6.1.10

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

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

Etapa 2.6.1.11

Add the terms together.

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

Etapa 2.6.2

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

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Etapa 2.6.2.1

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

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Etapa 2.6.2.1.1

Consider the corresponding sign chart.

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

Etapa 2.6.2.1.2

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

Etapa 2.6.2.1.3

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

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

Etapa 2.6.2.1.4

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

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

Etapa 2.6.2.1.5

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

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

Etapa 2.6.2.1.6

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

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

Etapa 2.6.2.1.7

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

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

Etapa 2.6.2.1.8

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

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

Etapa 2.6.2.1.9

Add the terms together.

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

Etapa 2.6.2.2

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

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Etapa 2.6.2.2.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Etapa 2.6.2.2.2

Simplifique o determinante.

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Etapa 2.6.2.2.2.1

Simplifique cada termo.

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Etapa 2.6.2.2.2.1.1

Multiplique $7$ por $143$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 (1001 - 175 \cdot 82) - 239 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} | + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.2.2.2.1.2

Multiplique $- 175$ por $82$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 (1001 - 14350) - 239 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} | + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.2.2.2.2

Subtraia $14350$ de $1001$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 \cdot - 13349 - 239 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} | + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.2.3

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

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Etapa 2.6.2.3.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 \cdot - 13349 - 239 (83 \cdot 143 - 20 \cdot 82) + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.2.3.2

Simplifique o determinante.

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Etapa 2.6.2.3.2.1

Simplifique cada termo.

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Etapa 2.6.2.3.2.1.1

Multiplique $83$ por $143$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 \cdot - 13349 - 239 (11869 - 20 \cdot 82) + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.2.3.2.1.2

Multiplique $- 20$ por $82$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 \cdot - 13349 - 239 (11869 - 1640) + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.2.3.2.2

Subtraia $1640$ de $11869$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 \cdot - 13349 - 239 \cdot 10229 + 218 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.2.4

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

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Etapa 2.6.2.4.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 \cdot - 13349 - 239 \cdot 10229 + 218 (83 \cdot 175 - 20 \cdot 7)) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.2.4.2

Simplifique o determinante.

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Etapa 2.6.2.4.2.1

Simplifique cada termo.

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Etapa 2.6.2.4.2.1.1

Multiplique $83$ por $175$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 \cdot - 13349 - 239 \cdot 10229 + 218 (14525 - 20 \cdot 7)) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.2.4.2.1.2

Multiplique $- 20$ por $7$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 \cdot - 13349 - 239 \cdot 10229 + 218 (14525 - 140)) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.2.4.2.2

Subtraia $140$ de $14525$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 82 \cdot - 13349 - 239 \cdot 10229 + 218 \cdot 14385) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.2.5

Simplifique o determinante.

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Etapa 2.6.2.5.1

Simplifique cada termo.

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Etapa 2.6.2.5.1.1

Multiplique $- 82$ por $- 13349$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (1094618 - 239 \cdot 10229 + 218 \cdot 14385) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.2.5.1.2

Multiplique $- 239$ por $10229$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (1094618 - 2444731 + 218 \cdot 14385) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.2.5.1.3

Multiplique $218$ por $14385$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (1094618 - 2444731 + 3135930) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.2.5.2

Subtraia $2444731$ de $1094618$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 (- 1350113 + 3135930) - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.2.5.3

Some $- 1350113$ e $3135930$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 | \begin{array}{c} 113 & 239 & 218 \\ 119 & 7 & 82 \\ 162 & 175 & 143 \end{array} | - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.3

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

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Etapa 2.6.3.1

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

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Etapa 2.6.3.1.1

Consider the corresponding sign chart.

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

Etapa 2.6.3.1.2

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

Etapa 2.6.3.1.3

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

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

Etapa 2.6.3.1.4

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

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

Etapa 2.6.3.1.5

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

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

Etapa 2.6.3.1.6

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

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

Etapa 2.6.3.1.7

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

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

Etapa 2.6.3.1.8

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

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

Etapa 2.6.3.1.9

Add the terms together.

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 | \begin{array}{c} 7 & 82 \\ 175 & 143 \end{array} | - 239 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.3.2

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

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Etapa 2.6.3.2.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 (7 \cdot 143 - 175 \cdot 82) - 239 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.3.2.2

Simplifique o determinante.

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Etapa 2.6.3.2.2.1

Simplifique cada termo.

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Etapa 2.6.3.2.2.1.1

Multiplique $7$ por $143$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 (1001 - 175 \cdot 82) - 239 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.3.2.2.1.2

Multiplique $- 175$ por $82$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 (1001 - 14350) - 239 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.3.2.2.2

Subtraia $14350$ de $1001$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 \cdot - 13349 - 239 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.3.3

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

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Etapa 2.6.3.3.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 \cdot - 13349 - 239 (119 \cdot 143 - 162 \cdot 82) + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.3.3.2

Simplifique o determinante.

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Etapa 2.6.3.3.2.1

Simplifique cada termo.

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Etapa 2.6.3.3.2.1.1

Multiplique $119$ por $143$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 \cdot - 13349 - 239 (17017 - 162 \cdot 82) + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.3.3.2.1.2

Multiplique $- 162$ por $82$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 \cdot - 13349 - 239 (17017 - 13284) + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.3.3.2.2

Subtraia $13284$ de $17017$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 \cdot - 13349 - 239 \cdot 3733 + 218 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.3.4

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

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Etapa 2.6.3.4.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 \cdot - 13349 - 239 \cdot 3733 + 218 (119 \cdot 175 - 162 \cdot 7)) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.3.4.2

Simplifique o determinante.

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Etapa 2.6.3.4.2.1

Simplifique cada termo.

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Etapa 2.6.3.4.2.1.1

Multiplique $119$ por $175$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 \cdot - 13349 - 239 \cdot 3733 + 218 (20825 - 162 \cdot 7)) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.3.4.2.1.2

Multiplique $- 162$ por $7$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 \cdot - 13349 - 239 \cdot 3733 + 218 (20825 - 1134)) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.3.4.2.2

Subtraia $1134$ de $20825$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (113 \cdot - 13349 - 239 \cdot 3733 + 218 \cdot 19691) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.3.5

Simplifique o determinante.

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Etapa 2.6.3.5.1

Simplifique cada termo.

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Etapa 2.6.3.5.1.1

Multiplique $113$ por $- 13349$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (- 1508437 - 239 \cdot 3733 + 218 \cdot 19691) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.3.5.1.2

Multiplique $- 239$ por $3733$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (- 1508437 - 892187 + 218 \cdot 19691) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.3.5.1.3

Multiplique $218$ por $19691$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (- 1508437 - 892187 + 4292638) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.3.5.2

Subtraia $892187$ de $- 1508437$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 (- 2400624 + 4292638) - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.3.5.3

Some $- 2400624$ e $4292638$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 | \begin{array}{c} 113 & - 82 & 218 \\ 119 & 83 & 82 \\ 162 & 20 & 143 \end{array} | - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.4

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

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Etapa 2.6.4.1

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

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Etapa 2.6.4.1.1

Consider the corresponding sign chart.

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

Etapa 2.6.4.1.2

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

Etapa 2.6.4.1.3

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

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

Etapa 2.6.4.1.4

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

$113 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |$

Etapa 2.6.4.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$

Etapa 2.6.4.1.6

Multiply element $a_{12}$ by its cofactor.

$82 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$

Etapa 2.6.4.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$

Etapa 2.6.4.1.8

Multiply element $a_{13}$ by its cofactor.

$218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$

Etapa 2.6.4.1.9

Add the terms together.

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 | \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} | + 82 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.4.2

Avalie $| \begin{array}{c} 83 & 82 \\ 20 & 143 \end{array} |$ .

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Etapa 2.6.4.2.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 (83 \cdot 143 - 20 \cdot 82) + 82 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.4.2.2

Simplifique o determinante.

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Etapa 2.6.4.2.2.1

Simplifique cada termo.

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Etapa 2.6.4.2.2.1.1

Multiplique $83$ por $143$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 (11869 - 20 \cdot 82) + 82 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.4.2.2.1.2

Multiplique $- 20$ por $82$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 (11869 - 1640) + 82 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.4.2.2.2

Subtraia $1640$ de $11869$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 \cdot 10229 + 82 | \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} | + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.4.3

Avalie $| \begin{array}{c} 119 & 82 \\ 162 & 143 \end{array} |$ .

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Etapa 2.6.4.3.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 \cdot 10229 + 82 (119 \cdot 143 - 162 \cdot 82) + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.4.3.2

Simplifique o determinante.

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Etapa 2.6.4.3.2.1

Simplifique cada termo.

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Etapa 2.6.4.3.2.1.1

Multiplique $119$ por $143$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 \cdot 10229 + 82 (17017 - 162 \cdot 82) + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.4.3.2.1.2

Multiplique $- 162$ por $82$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 \cdot 10229 + 82 (17017 - 13284) + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.4.3.2.2

Subtraia $13284$ de $17017$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 \cdot 10229 + 82 \cdot 3733 + 218 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.4.4

Avalie $| \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$ .

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Etapa 2.6.4.4.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 \cdot 10229 + 82 \cdot 3733 + 218 (119 \cdot 20 - 162 \cdot 83)) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.4.4.2

Simplifique o determinante.

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Etapa 2.6.4.4.2.1

Simplifique cada termo.

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Etapa 2.6.4.4.2.1.1

Multiplique $119$ por $20$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 \cdot 10229 + 82 \cdot 3733 + 218 (2380 - 162 \cdot 83)) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.4.4.2.1.2

Multiplique $- 162$ por $83$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 \cdot 10229 + 82 \cdot 3733 + 218 (2380 - 13446)) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.4.4.2.2

Subtraia $13446$ de $2380$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (113 \cdot 10229 + 82 \cdot 3733 + 218 \cdot - 11066) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.4.5

Simplifique o determinante.

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Etapa 2.6.4.5.1

Simplifique cada termo.

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Etapa 2.6.4.5.1.1

Multiplique $113$ por $10229$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (1155877 + 82 \cdot 3733 + 218 \cdot - 11066) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.4.5.1.2

Multiplique $82$ por $3733$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (1155877 + 306106 + 218 \cdot - 11066) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.4.5.1.3

Multiplique $218$ por $- 11066$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (1155877 + 306106 - 2412388) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.4.5.2

Some $1155877$ e $306106$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 (1461983 - 2412388) - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.4.5.3

Subtraia $2412388$ de $1461983$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 | \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |)$

Etapa 2.6.5

Avalie $| \begin{array}{c} 113 & - 82 & 239 \\ 119 & 83 & 7 \\ 162 & 20 & 175 \end{array} |$ .

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Etapa 2.6.5.1

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in row $1$ by its cofactor and add.

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Etapa 2.6.5.1.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Etapa 2.6.5.1.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Etapa 2.6.5.1.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$

Etapa 2.6.5.1.4

Multiply element $a_{11}$ by its cofactor.

$113 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$

Etapa 2.6.5.1.5

The minor for $a_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$

Etapa 2.6.5.1.6

Multiply element $a_{12}$ by its cofactor.

$82 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$

Etapa 2.6.5.1.7

The minor for $a_{13}$ is the determinant with row $1$ and column $3$ deleted.

$| \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$

Etapa 2.6.5.1.8

Multiply element $a_{13}$ by its cofactor.

$239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$

Etapa 2.6.5.1.9

Add the terms together.

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (113 | \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} | + 82 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} | + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |))$

Etapa 2.6.5.2

Avalie $| \begin{array}{c} 83 & 7 \\ 20 & 175 \end{array} |$ .

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Etapa 2.6.5.2.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (113 (83 \cdot 175 - 20 \cdot 7) + 82 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} | + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |))$

Etapa 2.6.5.2.2

Simplifique o determinante.

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Etapa 2.6.5.2.2.1

Simplifique cada termo.

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Etapa 2.6.5.2.2.1.1

Multiplique $83$ por $175$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (113 (14525 - 20 \cdot 7) + 82 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} | + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |))$

Etapa 2.6.5.2.2.1.2

Multiplique $- 20$ por $7$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (113 (14525 - 140) + 82 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} | + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |))$

Etapa 2.6.5.2.2.2

Subtraia $140$ de $14525$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (113 \cdot 14385 + 82 | \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} | + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |))$

Etapa 2.6.5.3

Avalie $| \begin{array}{c} 119 & 7 \\ 162 & 175 \end{array} |$ .

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Etapa 2.6.5.3.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (113 \cdot 14385 + 82 (119 \cdot 175 - 162 \cdot 7) + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |))$

Etapa 2.6.5.3.2

Simplifique o determinante.

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Etapa 2.6.5.3.2.1

Simplifique cada termo.

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Etapa 2.6.5.3.2.1.1

Multiplique $119$ por $175$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (113 \cdot 14385 + 82 (20825 - 162 \cdot 7) + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |))$

Etapa 2.6.5.3.2.1.2

Multiplique $- 162$ por $7$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (113 \cdot 14385 + 82 (20825 - 1134) + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |))$

Etapa 2.6.5.3.2.2

Subtraia $1134$ de $20825$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (113 \cdot 14385 + 82 \cdot 19691 + 239 | \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |))$

Etapa 2.6.5.4

Avalie $| \begin{array}{c} 119 & 83 \\ 162 & 20 \end{array} |$ .

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Etapa 2.6.5.4.1

O determinante de uma matriz $2 \times 2$ pode ser encontrado ao usar a fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

Etapa 2.6.5.4.2

Simplifique o determinante.

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Etapa 2.6.5.4.2.1

Simplifique cada termo.

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Etapa 2.6.5.4.2.1.1

Multiplique $119$ por $20$ .

Etapa 2.6.5.4.2.1.2

Multiplique $- 162$ por $83$ .

Etapa 2.6.5.4.2.2

Subtraia $13446$ de $2380$ .

Etapa 2.6.5.5

Simplifique o determinante.

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Etapa 2.6.5.5.1

Simplifique cada termo.

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Etapa 2.6.5.5.1.1

Multiplique $113$ por $14385$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (1625505 + 82 \cdot 19691 + 239 \cdot - 11066))$

Etapa 2.6.5.5.1.2

Multiplique $82$ por $19691$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (1625505 + 1614662 + 239 \cdot - 11066))$

Etapa 2.6.5.5.1.3

Multiplique $239$ por $- 11066$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (1625505 + 1614662 - 2644774))$

Etapa 2.6.5.5.2

Some $1625505$ e $1614662$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 (3240167 - 2644774))$

Etapa 2.6.5.5.3

Subtraia $2644774$ de $3240167$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (20 \cdot 1785817 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 \cdot 595393)$

Etapa 2.6.6

Simplifique o determinante.

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Etapa 2.6.6.1

Simplifique cada termo.

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Etapa 2.6.6.1.1

Multiplique $20$ por $1785817$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (35716340 - 169 \cdot 1892014 - 164 \cdot - 950405 - 18 \cdot 595393)$

Etapa 2.6.6.1.2

Multiplique $- 169$ por $1892014$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (35716340 - 319750366 - 164 \cdot - 950405 - 18 \cdot 595393)$

Etapa 2.6.6.1.3

Multiplique $- 164$ por $- 950405$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (35716340 - 319750366 + 155866420 - 18 \cdot 595393)$

Etapa 2.6.6.1.4

Multiplique $- 18$ por $595393$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (35716340 - 319750366 + 155866420 - 10717074)$

Etapa 2.6.6.2

Subtraia $319750366$ de $35716340$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (- 284034026 + 155866420 - 10717074)$

Etapa 2.6.6.3

Some $- 284034026$ e $155866420$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 (- 128167606 - 10717074)$

Etapa 2.6.6.4

Subtraia $10717074$ de $- 128167606$ .

$44 \cdot 115002558 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 \cdot - 138884680$

Etapa 2.7

Simplifique o determinante.

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Etapa 2.7.1

Simplifique cada termo.

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Etapa 2.7.1.1

Multiplique $44$ por $115002558$ .

$5060112552 - 75 \cdot - 72015204 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 \cdot - 138884680$

Etapa 2.7.1.2

Multiplique $- 75$ por $- 72015204$ .

$5060112552 + 5401140300 - 60 \cdot - 7230030 + 33 \cdot 59636342 + 11 \cdot - 138884680$

Etapa 2.7.1.3

Multiplique $- 60$ por $- 7230030$ .

$5060112552 + 5401140300 + 433801800 + 33 \cdot 59636342 + 11 \cdot - 138884680$

Etapa 2.7.1.4

Multiplique $33$ por $59636342$ .

$5060112552 + 5401140300 + 433801800 + 1967999286 + 11 \cdot - 138884680$

Etapa 2.7.1.5

Multiplique $11$ por $- 138884680$ .

$5060112552 + 5401140300 + 433801800 + 1967999286 - 1527731480$

Etapa 2.7.2

Some $5060112552$ e $5401140300$ .

$10461252852 + 433801800 + 1967999286 - 1527731480$

Etapa 2.7.3

Some $10461252852$ e $433801800$ .

$10895054652 + 1967999286 - 1527731480$

Etapa 2.7.4

Some $10895054652$ e $1967999286$ .

$12863053938 - 1527731480$

Etapa 2.7.5

Subtraia $1527731480$ de $12863053938$ .

$11335322458$

Etapa 3

Since the determinant is non-zero, the inverse exists.

Etapa 4

Set up a $5 \times 10$ matrix where the left half is the original matrix and the right half is its identity matrix.

$[\begin{array}{c} 44 & 75 & - 60 & - 33 & 11 & 1 & 0 & 0 & 0 & 0 \\ 20 & 169 & - 164 & 18 & 105 & 0 & 1 & 0 & 0 & 0 \\ 113 & - 82 & 239 & 218 & - 55 & 0 & 0 & 1 & 0 & 0 \\ 119 & 83 & 7 & 82 & 106 & 0 & 0 & 0 & 1 & 0 \\ 162 & 20 & 175 & 143 & 74 & 0 & 0 & 0 & 0 & 1 \end{array}]$

Etapa 5

Encontre a forma escalonada reduzida por linhas.

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Etapa 5.1

Multiply each element of $R_{1}$ by $\frac{1}{44}$ to make the entry at $1, 1$ a $1$ .

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Etapa 5.1.1

Multiply each element of $R_{1}$ by $\frac{1}{44}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{44}{44} & \frac{75}{44} & \frac{- 60}{44} & \frac{- 33}{44} & \frac{11}{44} & \frac{1}{44} & \frac{0}{44} & \frac{0}{44} & \frac{0}{44} & \frac{0}{44} \\ 20 & 169 & - 164 & 18 & 105 & 0 & 1 & 0 & 0 & 0 \\ 113 & - 82 & 239 & 218 & - 55 & 0 & 0 & 1 & 0 & 0 \\ 119 & 83 & 7 & 82 & 106 & 0 & 0 & 0 & 1 & 0 \\ 162 & 20 & 175 & 143 & 74 & 0 & 0 & 0 & 0 & 1 \end{array}]$

Etapa 5.1.2

Simplifique $R_{1}$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 20 & 169 & - 164 & 18 & 105 & 0 & 1 & 0 & 0 & 0 \\ 113 & - 82 & 239 & 218 & - 55 & 0 & 0 & 1 & 0 & 0 \\ 119 & 83 & 7 & 82 & 106 & 0 & 0 & 0 & 1 & 0 \\ 162 & 20 & 175 & 143 & 74 & 0 & 0 & 0 & 0 & 1 \end{array}]$

Etapa 5.2

Perform the row operation $R_{2} = R_{2} - 20 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Etapa 5.2.1

Perform the row operation $R_{2} = R_{2} - 20 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 20 - 20 \cdot 1 & 169 - 20 (\frac{75}{44}) & - 164 - 20 (- \frac{15}{11}) & 18 - 20 (- \frac{3}{4}) & 105 - 20 (\frac{1}{4}) & 0 - 20 (\frac{1}{44}) & 1 - 20 \cdot 0 & 0 - 20 \cdot 0 & 0 - 20 \cdot 0 & 0 - 20 \cdot 0 \\ 113 & - 82 & 239 & 218 & - 55 & 0 & 0 & 1 & 0 & 0 \\ 119 & 83 & 7 & 82 & 106 & 0 & 0 & 0 & 1 & 0 \\ 162 & 20 & 175 & 143 & 74 & 0 & 0 & 0 & 0 & 1 \end{array}]$

Etapa 5.2.2

Simplifique $R_{2}$ .

Etapa 5.3

Perform the row operation $R_{3} = R_{3} - 113 R_{1}$ to make the entry at $3, 1$ a $0$ .

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Etapa 5.3.1

Perform the row operation $R_{3} = R_{3} - 113 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & \frac{1484}{11} & - \frac{1504}{11} & 33 & 100 & - \frac{5}{11} & 1 & 0 & 0 & 0 \\ 113 - 113 \cdot 1 & - 82 - 113 (\frac{75}{44}) & 239 - 113 (- \frac{15}{11}) & 218 - 113 (- \frac{3}{4}) & - 55 - 113 (\frac{1}{4}) & 0 - 113 (\frac{1}{44}) & 0 - 113 \cdot 0 & 1 - 113 \cdot 0 & 0 - 113 \cdot 0 & 0 - 113 \cdot 0 \\ 119 & 83 & 7 & 82 & 106 & 0 & 0 & 0 & 1 & 0 \\ 162 & 20 & 175 & 143 & 74 & 0 & 0 & 0 & 0 & 1 \end{array}]$

Etapa 5.3.2

Simplifique $R_{3}$ .

Etapa 5.4

Perform the row operation $R_{4} = R_{4} - 119 R_{1}$ to make the entry at $4, 1$ a $0$ .

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Etapa 5.4.1

Perform the row operation $R_{4} = R_{4} - 119 R_{1}$ to make the entry at $4, 1$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & \frac{1484}{11} & - \frac{1504}{11} & 33 & 100 & - \frac{5}{11} & 1 & 0 & 0 & 0 \\ 0 & - \frac{12083}{44} & \frac{4324}{11} & \frac{1211}{4} & - \frac{333}{4} & - \frac{113}{44} & 0 & 1 & 0 & 0 \\ 119 - 119 \cdot 1 & 83 - 119 (\frac{75}{44}) & 7 - 119 (- \frac{15}{11}) & 82 - 119 (- \frac{3}{4}) & 106 - 119 (\frac{1}{4}) & 0 - 119 (\frac{1}{44}) & 0 - 119 \cdot 0 & 0 - 119 \cdot 0 & 1 - 119 \cdot 0 & 0 - 119 \cdot 0 \\ 162 & 20 & 175 & 143 & 74 & 0 & 0 & 0 & 0 & 1 \end{array}]$

Etapa 5.4.2

Simplifique $R_{4}$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & \frac{1484}{11} & - \frac{1504}{11} & 33 & 100 & - \frac{5}{11} & 1 & 0 & 0 & 0 \\ 0 & - \frac{12083}{44} & \frac{4324}{11} & \frac{1211}{4} & - \frac{333}{4} & - \frac{113}{44} & 0 & 1 & 0 & 0 \\ 0 & - \frac{5273}{44} & \frac{1862}{11} & \frac{685}{4} & \frac{305}{4} & - \frac{119}{44} & 0 & 0 & 1 & 0 \\ 162 & 20 & 175 & 143 & 74 & 0 & 0 & 0 & 0 & 1 \end{array}]$

Etapa 5.5

Perform the row operation $R_{5} = R_{5} - 162 R_{1}$ to make the entry at $5, 1$ a $0$ .

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Etapa 5.5.1

Perform the row operation $R_{5} = R_{5} - 162 R_{1}$ to make the entry at $5, 1$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & \frac{1484}{11} & - \frac{1504}{11} & 33 & 100 & - \frac{5}{11} & 1 & 0 & 0 & 0 \\ 0 & - \frac{12083}{44} & \frac{4324}{11} & \frac{1211}{4} & - \frac{333}{4} & - \frac{113}{44} & 0 & 1 & 0 & 0 \\ 0 & - \frac{5273}{44} & \frac{1862}{11} & \frac{685}{4} & \frac{305}{4} & - \frac{119}{44} & 0 & 0 & 1 & 0 \\ 162 - 162 \cdot 1 & 20 - 162 (\frac{75}{44}) & 175 - 162 (- \frac{15}{11}) & 143 - 162 (- \frac{3}{4}) & 74 - 162 (\frac{1}{4}) & 0 - 162 (\frac{1}{44}) & 0 - 162 \cdot 0 & 0 - 162 \cdot 0 & 0 - 162 \cdot 0 & 1 - 162 \cdot 0 \end{array}]$

Etapa 5.5.2

Simplifique $R_{5}$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & \frac{1484}{11} & - \frac{1504}{11} & 33 & 100 & - \frac{5}{11} & 1 & 0 & 0 & 0 \\ 0 & - \frac{12083}{44} & \frac{4324}{11} & \frac{1211}{4} & - \frac{333}{4} & - \frac{113}{44} & 0 & 1 & 0 & 0 \\ 0 & - \frac{5273}{44} & \frac{1862}{11} & \frac{685}{4} & \frac{305}{4} & - \frac{119}{44} & 0 & 0 & 1 & 0 \\ 0 & - \frac{5635}{22} & \frac{4355}{11} & \frac{529}{2} & \frac{67}{2} & - \frac{81}{22} & 0 & 0 & 0 & 1 \end{array}]$

Etapa 5.6

Multiply each element of $R_{2}$ by $\frac{11}{1484}$ to make the entry at $2, 2$ a $1$ .

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Etapa 5.6.1

Multiply each element of $R_{2}$ by $\frac{11}{1484}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ \frac{11}{1484} \cdot 0 & \frac{11}{1484} \cdot \frac{1484}{11} & \frac{11}{1484} (- \frac{1504}{11}) & \frac{11}{1484} \cdot 33 & \frac{11}{1484} \cdot 100 & \frac{11}{1484} (- \frac{5}{11}) & \frac{11}{1484} \cdot 1 & \frac{11}{1484} \cdot 0 & \frac{11}{1484} \cdot 0 & \frac{11}{1484} \cdot 0 \\ 0 & - \frac{12083}{44} & \frac{4324}{11} & \frac{1211}{4} & - \frac{333}{4} & - \frac{113}{44} & 0 & 1 & 0 & 0 \\ 0 & - \frac{5273}{44} & \frac{1862}{11} & \frac{685}{4} & \frac{305}{4} & - \frac{119}{44} & 0 & 0 & 1 & 0 \\ 0 & - \frac{5635}{22} & \frac{4355}{11} & \frac{529}{2} & \frac{67}{2} & - \frac{81}{22} & 0 & 0 & 0 & 1 \end{array}]$

Etapa 5.6.2

Simplifique $R_{2}$ .

Etapa 5.7

Perform the row operation $R_{3} = R_{3} + \frac{12083}{44} R_{2}$ to make the entry at $3, 2$ a $0$ .

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Etapa 5.7.1

Perform the row operation $R_{3} = R_{3} + \frac{12083}{44} R_{2}$ to make the entry at $3, 2$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 + \frac{12083}{44} \cdot 0 & - \frac{12083}{44} + \frac{12083}{44} \cdot 1 & \frac{4324}{11} + \frac{12083}{44} (- \frac{376}{371}) & \frac{1211}{4} + \frac{12083}{44} \cdot \frac{363}{1484} & - \frac{333}{4} + \frac{12083}{44} \cdot \frac{275}{371} & - \frac{113}{44} + \frac{12083}{44} (- \frac{5}{1484}) & 0 + \frac{12083}{44} \cdot \frac{11}{1484} & 1 + \frac{12083}{44} \cdot 0 & 0 + \frac{12083}{44} \cdot 0 & 0 + \frac{12083}{44} \cdot 0 \\ 0 & - \frac{5273}{44} & \frac{1862}{11} & \frac{685}{4} & \frac{305}{4} & - \frac{119}{44} & 0 & 0 & 1 & 0 \\ 0 & - \frac{5635}{22} & \frac{4355}{11} & \frac{529}{2} & \frac{67}{2} & - \frac{81}{22} & 0 & 0 & 0 & 1 \end{array}]$

Etapa 5.7.2

Simplifique $R_{3}$ .

Etapa 5.8

Perform the row operation $R_{4} = R_{4} + \frac{5273}{44} R_{2}$ to make the entry at $4, 2$ a $0$ .

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Etapa 5.8.1

Perform the row operation $R_{4} = R_{4} + \frac{5273}{44} R_{2}$ to make the entry at $4, 2$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 & 0 & \frac{42582}{371} & \frac{2195863}{5936} & \frac{44633}{371} & - \frac{20737}{5936} & \frac{12083}{5936} & 1 & 0 & 0 \\ 0 + \frac{5273}{44} \cdot 0 & - \frac{5273}{44} + \frac{5273}{44} \cdot 1 & \frac{1862}{11} + \frac{5273}{44} (- \frac{376}{371}) & \frac{685}{4} + \frac{5273}{44} \cdot \frac{363}{1484} & \frac{305}{4} + \frac{5273}{44} \cdot \frac{275}{371} & - \frac{119}{44} + \frac{5273}{44} (- \frac{5}{1484}) & 0 + \frac{5273}{44} \cdot \frac{11}{1484} & 0 + \frac{5273}{44} \cdot 0 & 1 + \frac{5273}{44} \cdot 0 & 0 + \frac{5273}{44} \cdot 0 \\ 0 & - \frac{5635}{22} & \frac{4355}{11} & \frac{529}{2} & \frac{67}{2} & - \frac{81}{22} & 0 & 0 & 0 & 1 \end{array}]$

Etapa 5.8.2

Simplifique $R_{4}$ .

Etapa 5.9

Perform the row operation $R_{5} = R_{5} + \frac{5635}{22} R_{2}$ to make the entry at $5, 2$ a $0$ .

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Etapa 5.9.1

Perform the row operation $R_{5} = R_{5} + \frac{5635}{22} R_{2}$ to make the entry at $5, 2$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 & 0 & \frac{42582}{371} & \frac{2195863}{5936} & \frac{44633}{371} & - \frac{20737}{5936} & \frac{12083}{5936} & 1 & 0 & 0 \\ 0 & 0 & \frac{17740}{371} & \frac{1190549}{5936} & \frac{61245}{371} & - \frac{18451}{5936} & \frac{5273}{5936} & 0 & 1 & 0 \\ 0 + \frac{5635}{22} \cdot 0 & - \frac{5635}{22} + \frac{5635}{22} \cdot 1 & \frac{4355}{11} + \frac{5635}{22} (- \frac{376}{371}) & \frac{529}{2} + \frac{5635}{22} \cdot \frac{363}{1484} & \frac{67}{2} + \frac{5635}{22} \cdot \frac{275}{371} & - \frac{81}{22} + \frac{5635}{22} (- \frac{5}{1484}) & 0 + \frac{5635}{22} \cdot \frac{11}{1484} & 0 + \frac{5635}{22} \cdot 0 & 0 + \frac{5635}{22} \cdot 0 & 1 + \frac{5635}{22} \cdot 0 \end{array}]$

Etapa 5.9.2

Simplifique $R_{5}$ .

Etapa 5.10

Multiply each element of $R_{3}$ by $\frac{371}{42582}$ to make the entry at $3, 3$ a $1$ .

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Etapa 5.10.1

Multiply each element of $R_{3}$ by $\frac{371}{42582}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ \frac{371}{42582} \cdot 0 & \frac{371}{42582} \cdot 0 & \frac{371}{42582} \cdot \frac{42582}{371} & \frac{371}{42582} \cdot \frac{2195863}{5936} & \frac{371}{42582} \cdot \frac{44633}{371} & \frac{371}{42582} (- \frac{20737}{5936}) & \frac{371}{42582} \cdot \frac{12083}{5936} & \frac{371}{42582} \cdot 1 & \frac{371}{42582} \cdot 0 & \frac{371}{42582} \cdot 0 \\ 0 & 0 & \frac{17740}{371} & \frac{1190549}{5936} & \frac{61245}{371} & - \frac{18451}{5936} & \frac{5273}{5936} & 0 & 1 & 0 \\ 0 & 0 & \frac{7225}{53} & \frac{138713}{424} & \frac{11838}{53} & - \frac{1927}{424} & \frac{805}{424} & 0 & 0 & 1 \end{array}]$

Etapa 5.10.2

Simplifique $R_{3}$ .

Etapa 5.11

Perform the row operation $R_{4} = R_{4} - \frac{17740}{371} R_{3}$ to make the entry at $4, 3$ a $0$ .

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Etapa 5.11.1

Perform the row operation $R_{4} = R_{4} - \frac{17740}{371} R_{3}$ to make the entry at $4, 3$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{2195863}{681312} & \frac{44633}{42582} & - \frac{20737}{681312} & \frac{12083}{681312} & \frac{371}{42582} & 0 & 0 \\ 0 - \frac{17740}{371} \cdot 0 & 0 - \frac{17740}{371} \cdot 0 & \frac{17740}{371} - \frac{17740}{371} \cdot 1 & \frac{1190549}{5936} - \frac{17740}{371} \cdot \frac{2195863}{681312} & \frac{61245}{371} - \frac{17740}{371} \cdot \frac{44633}{42582} & - \frac{18451}{5936} - \frac{17740}{371} (- \frac{20737}{681312}) & \frac{5273}{5936} - \frac{17740}{371} \cdot \frac{12083}{681312} & 0 - \frac{17740}{371} \cdot \frac{371}{42582} & 1 - \frac{17740}{371} \cdot 0 & 0 - \frac{17740}{371} \cdot 0 \\ 0 & 0 & \frac{7225}{53} & \frac{138713}{424} & \frac{11838}{53} & - \frac{1927}{424} & \frac{805}{424} & 0 & 0 & 1 \end{array}]$

Etapa 5.11.2

Simplifique $R_{4}$ .

Etapa 5.12

Perform the row operation $R_{5} = R_{5} - \frac{7225}{53} R_{3}$ to make the entry at $5, 3$ a $0$ .

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Etapa 5.12.1

Perform the row operation $R_{5} = R_{5} - \frac{7225}{53} R_{3}$ to make the entry at $5, 3$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{2195863}{681312} & \frac{44633}{42582} & - \frac{20737}{681312} & \frac{12083}{681312} & \frac{371}{42582} & 0 & 0 \\ 0 & 0 & 0 & \frac{15823919}{340656} & \frac{2447635}{21291} & - \frac{563081}{340656} & \frac{13723}{340656} & - \frac{8870}{21291} & 1 & 0 \\ 0 - \frac{7225}{53} \cdot 0 & 0 - \frac{7225}{53} \cdot 0 & \frac{7225}{53} - \frac{7225}{53} \cdot 1 & \frac{138713}{424} - \frac{7225}{53} \cdot \frac{2195863}{681312} & \frac{11838}{53} - \frac{7225}{53} \cdot \frac{44633}{42582} & - \frac{1927}{424} - \frac{7225}{53} (- \frac{20737}{681312}) & \frac{805}{424} - \frac{7225}{53} \cdot \frac{12083}{681312} & 0 - \frac{7225}{53} \cdot \frac{371}{42582} & 0 - \frac{7225}{53} \cdot 0 & 1 - \frac{7225}{53} \cdot 0 \end{array}]$

Etapa 5.12.2

Simplifique $R_{5}$ .

Etapa 5.13

Multiply each element of $R_{4}$ by $\frac{340656}{15823919}$ to make the entry at $4, 4$ a $1$ .

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Etapa 5.13.1

Multiply each element of $R_{4}$ by $\frac{340656}{15823919}$ to make the entry at $4, 4$ a $1$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{2195863}{681312} & \frac{44633}{42582} & - \frac{20737}{681312} & \frac{12083}{681312} & \frac{371}{42582} & 0 & 0 \\ \frac{340656}{15823919} \cdot 0 & \frac{340656}{15823919} \cdot 0 & \frac{340656}{15823919} \cdot 0 & \frac{340656}{15823919} \cdot \frac{15823919}{340656} & \frac{340656}{15823919} \cdot \frac{2447635}{21291} & \frac{340656}{15823919} (- \frac{563081}{340656}) & \frac{340656}{15823919} \cdot \frac{13723}{340656} & \frac{340656}{15823919} (- \frac{8870}{21291}) & \frac{340656}{15823919} \cdot 1 & \frac{340656}{15823919} \cdot 0 \\ 0 & 0 & 0 & - \frac{76448231}{681312} & \frac{3426647}{42582} & - \frac{269551}{681312} & - \frac{353635}{681312} & - \frac{50575}{42582} & 0 & 1 \end{array}]$

Etapa 5.13.2

Simplifique $R_{4}$ .

Etapa 5.14

Perform the row operation $R_{5} = R_{5} + \frac{76448231}{681312} R_{4}$ to make the entry at $5, 4$ a $0$ .

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Etapa 5.14.1

Perform the row operation $R_{5} = R_{5} + \frac{76448231}{681312} R_{4}$ to make the entry at $5, 4$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{2195863}{681312} & \frac{44633}{42582} & - \frac{20737}{681312} & \frac{12083}{681312} & \frac{371}{42582} & 0 & 0 \\ 0 & 0 & 0 & 1 & \frac{39162160}{15823919} & - \frac{563081}{15823919} & \frac{13723}{15823919} & - \frac{141920}{15823919} & \frac{340656}{15823919} & 0 \\ 0 + \frac{76448231}{681312} \cdot 0 & 0 + \frac{76448231}{681312} \cdot 0 & 0 + \frac{76448231}{681312} \cdot 0 & - \frac{76448231}{681312} + \frac{76448231}{681312} \cdot 1 & \frac{3426647}{42582} + \frac{76448231}{681312} \cdot \frac{39162160}{15823919} & - \frac{269551}{681312} + \frac{76448231}{681312} (- \frac{563081}{15823919}) & - \frac{353635}{681312} + \frac{76448231}{681312} \cdot \frac{13723}{15823919} & - \frac{50575}{42582} + \frac{76448231}{681312} (- \frac{141920}{15823919}) & 0 + \frac{76448231}{681312} \cdot \frac{340656}{15823919} & 1 + \frac{76448231}{681312} \cdot 0 \end{array}]$

Etapa 5.14.2

Simplifique $R_{5}$ .

Etapa 5.15

Multiply each element of $R_{5}$ by $\frac{15823919}{5667661229}$ to make the entry at $5, 5$ a $1$ .

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Etapa 5.15.1

Multiply each element of $R_{5}$ by $\frac{15823919}{5667661229}$ to make the entry at $5, 5$ a $1$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{2195863}{681312} & \frac{44633}{42582} & - \frac{20737}{681312} & \frac{12083}{681312} & \frac{371}{42582} & 0 & 0 \\ 0 & 0 & 0 & 1 & \frac{39162160}{15823919} & - \frac{563081}{15823919} & \frac{13723}{15823919} & - \frac{141920}{15823919} & \frac{340656}{15823919} & 0 \\ \frac{15823919}{5667661229} \cdot 0 & \frac{15823919}{5667661229} \cdot 0 & \frac{15823919}{5667661229} \cdot 0 & \frac{15823919}{5667661229} \cdot 0 & \frac{15823919}{5667661229} \cdot \frac{5667661229}{15823919} & \frac{15823919}{5667661229} (- \frac{69442340}{15823919}) & \frac{15823919}{5667661229} (- \frac{13347167}{31647838}) & \frac{15823919}{5667661229} (- \frac{69437345}{31647838}) & \frac{15823919}{5667661229} \cdot \frac{76448231}{31647838} & \frac{15823919}{5667661229} \cdot 1 \end{array}]$

Etapa 5.15.2

Simplifique $R_{5}$ .

Etapa 5.16

Perform the row operation $R_{4} = R_{4} - \frac{39162160}{15823919} R_{5}$ to make the entry at $4, 5$ a $0$ .

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Etapa 5.16.1

Perform the row operation $R_{4} = R_{4} - \frac{39162160}{15823919} R_{5}$ to make the entry at $4, 5$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{2195863}{681312} & \frac{44633}{42582} & - \frac{20737}{681312} & \frac{12083}{681312} & \frac{371}{42582} & 0 & 0 \\ 0 - \frac{39162160}{15823919} \cdot 0 & 0 - \frac{39162160}{15823919} \cdot 0 & 0 - \frac{39162160}{15823919} \cdot 0 & 1 - \frac{39162160}{15823919} \cdot 0 & \frac{39162160}{15823919} - \frac{39162160}{15823919} \cdot 1 & - \frac{563081}{15823919} - \frac{39162160}{15823919} (- \frac{69442340}{5667661229}) & \frac{13723}{15823919} - \frac{39162160}{15823919} (- \frac{13347167}{11335322458}) & - \frac{141920}{15823919} - \frac{39162160}{15823919} (- \frac{69437345}{11335322458}) & \frac{340656}{15823919} - \frac{39162160}{15823919} \cdot \frac{76448231}{11335322458} & 0 - \frac{39162160}{15823919} \cdot \frac{15823919}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Etapa 5.16.2

Simplifique $R_{4}$ .

Etapa 5.17

Perform the row operation $R_{3} = R_{3} - \frac{44633}{42582} R_{5}$ to make the entry at $3, 5$ a $0$ .

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Etapa 5.17.1

Perform the row operation $R_{3} = R_{3} - \frac{44633}{42582} R_{5}$ to make the entry at $3, 5$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 - \frac{44633}{42582} \cdot 0 & 0 - \frac{44633}{42582} \cdot 0 & 1 - \frac{44633}{42582} \cdot 0 & \frac{2195863}{681312} - \frac{44633}{42582} \cdot 0 & \frac{44633}{42582} - \frac{44633}{42582} \cdot 1 & - \frac{20737}{681312} - \frac{44633}{42582} (- \frac{69442340}{5667661229}) & \frac{12083}{681312} - \frac{44633}{42582} (- \frac{13347167}{11335322458}) & \frac{371}{42582} - \frac{44633}{42582} (- \frac{69437345}{11335322458}) & 0 - \frac{44633}{42582} \cdot \frac{76448231}{11335322458} & 0 - \frac{44633}{42582} \cdot \frac{15823919}{5667661229} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Etapa 5.17.2

Simplifique $R_{3}$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & \frac{275}{371} & - \frac{5}{1484} & \frac{11}{1484} & 0 & 0 & 0 \\ 0 & 0 & 1 & \frac{2195863}{681312} & 0 & - \frac{67939571526253}{3861445607252448} & \frac{24416047822565}{1287148535750816} & \frac{2434867217101}{160893566968852} & - \frac{3412113894223}{482680700906556} & - \frac{706268976727}{241340350453278} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Etapa 5.18

Perform the row operation $R_{2} = R_{2} - \frac{275}{371} R_{5}$ to make the entry at $2, 5$ a $0$ .

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Etapa 5.18.1

Perform the row operation $R_{2} = R_{2} - \frac{275}{371} R_{5}$ to make the entry at $2, 5$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 - \frac{275}{371} \cdot 0 & 1 - \frac{275}{371} \cdot 0 & - \frac{376}{371} - \frac{275}{371} \cdot 0 & \frac{363}{1484} - \frac{275}{371} \cdot 0 & \frac{275}{371} - \frac{275}{371} \cdot 1 & - \frac{5}{1484} - \frac{275}{371} (- \frac{69442340}{5667661229}) & \frac{11}{1484} - \frac{275}{371} (- \frac{13347167}{11335322458}) & 0 - \frac{275}{371} (- \frac{69437345}{11335322458}) & 0 - \frac{275}{371} \cdot \frac{76448231}{11335322458} & 0 - \frac{275}{371} \cdot \frac{15823919}{5667661229} \\ 0 & 0 & 1 & \frac{2195863}{681312} & 0 & - \frac{67939571526253}{3861445607252448} & \frac{24416047822565}{1287148535750816} & \frac{2434867217101}{160893566968852} & - \frac{3412113894223}{482680700906556} & - \frac{706268976727}{241340350453278} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Etapa 5.18.2

Simplifique $R_{2}$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & \frac{1}{4} & \frac{1}{44} & 0 & 0 & 0 & 0 \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & 0 & \frac{6864038265}{1201544180548} & \frac{9955030767}{1201544180548} & \frac{19095269875}{4205404631918} & - \frac{21023263525}{4205404631918} & - \frac{4351577725}{2102702315959} \\ 0 & 0 & 1 & \frac{2195863}{681312} & 0 & - \frac{67939571526253}{3861445607252448} & \frac{24416047822565}{1287148535750816} & \frac{2434867217101}{160893566968852} & - \frac{3412113894223}{482680700906556} & - \frac{706268976727}{241340350453278} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Etapa 5.19

Perform the row operation $R_{1} = R_{1} - \frac{1}{4} R_{5}$ to make the entry at $1, 5$ a $0$ .

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Etapa 5.19.1

Perform the row operation $R_{1} = R_{1} - \frac{1}{4} R_{5}$ to make the entry at $1, 5$ a $0$ .

$[\begin{array}{c} 1 - \frac{1}{4} \cdot 0 & \frac{75}{44} - \frac{1}{4} \cdot 0 & - \frac{15}{11} - \frac{1}{4} \cdot 0 & - \frac{3}{4} - \frac{1}{4} \cdot 0 & \frac{1}{4} - \frac{1}{4} \cdot 1 & \frac{1}{44} - \frac{1}{4} (- \frac{69442340}{5667661229}) & 0 - \frac{1}{4} (- \frac{13347167}{11335322458}) & 0 - \frac{1}{4} (- \frac{69437345}{11335322458}) & 0 - \frac{1}{4} \cdot \frac{76448231}{11335322458} & 0 - \frac{1}{4} \cdot \frac{15823919}{5667661229} \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & 0 & \frac{6864038265}{1201544180548} & \frac{9955030767}{1201544180548} & \frac{19095269875}{4205404631918} & - \frac{21023263525}{4205404631918} & - \frac{4351577725}{2102702315959} \\ 0 & 0 & 1 & \frac{2195863}{681312} & 0 & - \frac{67939571526253}{3861445607252448} & \frac{24416047822565}{1287148535750816} & \frac{2434867217101}{160893566968852} & - \frac{3412113894223}{482680700906556} & - \frac{706268976727}{241340350453278} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Etapa 5.19.2

Simplifique $R_{1}$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & 0 & \frac{6431526969}{249377094076} & \frac{13347167}{45341289832} & \frac{69437345}{45341289832} & - \frac{76448231}{45341289832} & - \frac{15823919}{22670644916} \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & 0 & \frac{6864038265}{1201544180548} & \frac{9955030767}{1201544180548} & \frac{19095269875}{4205404631918} & - \frac{21023263525}{4205404631918} & - \frac{4351577725}{2102702315959} \\ 0 & 0 & 1 & \frac{2195863}{681312} & 0 & - \frac{67939571526253}{3861445607252448} & \frac{24416047822565}{1287148535750816} & \frac{2434867217101}{160893566968852} & - \frac{3412113894223}{482680700906556} & - \frac{706268976727}{241340350453278} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Etapa 5.20

Perform the row operation $R_{3} = R_{3} - \frac{2195863}{681312} R_{4}$ to make the entry at $3, 4$ a $0$ .

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Etapa 5.20.1

Perform the row operation $R_{3} = R_{3} - \frac{2195863}{681312} R_{4}$ to make the entry at $3, 4$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & 0 & \frac{6431526969}{249377094076} & \frac{13347167}{45341289832} & \frac{69437345}{45341289832} & - \frac{76448231}{45341289832} & - \frac{15823919}{22670644916} \\ 0 & 1 & - \frac{376}{371} & \frac{363}{1484} & 0 & \frac{6864038265}{1201544180548} & \frac{9955030767}{1201544180548} & \frac{19095269875}{4205404631918} & - \frac{21023263525}{4205404631918} & - \frac{4351577725}{2102702315959} \\ 0 - \frac{2195863}{681312} \cdot 0 & 0 - \frac{2195863}{681312} \cdot 0 & 1 - \frac{2195863}{681312} \cdot 0 & \frac{2195863}{681312} - \frac{2195863}{681312} \cdot 1 & 0 - \frac{2195863}{681312} \cdot 0 & - \frac{67939571526253}{3861445607252448} - \frac{2195863}{681312} (- \frac{29818171}{5667661229}) & \frac{24416047822565}{1287148535750816} - \frac{2195863}{681312} \cdot \frac{21431433}{5667661229} & \frac{2434867217101}{160893566968852} - \frac{2195863}{681312} \cdot \frac{35092680}{5667661229} & - \frac{3412113894223}{482680700906556} - \frac{2195863}{681312} \cdot \frac{27413176}{5667661229} & - \frac{706268976727}{241340350453278} - \frac{2195863}{681312} (- \frac{39162160}{5667661229}) \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Etapa 5.20.2

Simplifique $R_{3}$ .

Etapa 5.21

Perform the row operation $R_{2} = R_{2} - \frac{363}{1484} R_{4}$ to make the entry at $2, 4$ a $0$ .

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Etapa 5.21.1

Perform the row operation $R_{2} = R_{2} - \frac{363}{1484} R_{4}$ to make the entry at $2, 4$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & - \frac{3}{4} & 0 & \frac{6431526969}{249377094076} & \frac{13347167}{45341289832} & \frac{69437345}{45341289832} & - \frac{76448231}{45341289832} & - \frac{15823919}{22670644916} \\ 0 - \frac{363}{1484} \cdot 0 & 1 - \frac{363}{1484} \cdot 0 & - \frac{376}{371} - \frac{363}{1484} \cdot 0 & \frac{363}{1484} - \frac{363}{1484} \cdot 1 & 0 - \frac{363}{1484} \cdot 0 & \frac{6864038265}{1201544180548} - \frac{363}{1484} (- \frac{29818171}{5667661229}) & \frac{9955030767}{1201544180548} - \frac{363}{1484} \cdot \frac{21431433}{5667661229} & \frac{19095269875}{4205404631918} - \frac{363}{1484} \cdot \frac{35092680}{5667661229} & - \frac{21023263525}{4205404631918} - \frac{363}{1484} \cdot \frac{27413176}{5667661229} & - \frac{4351577725}{2102702315959} - \frac{363}{1484} (- \frac{39162160}{5667661229}) \\ 0 & 0 & 1 & 0 & 0 & - \frac{3615015}{5667661229} & \frac{38437093}{5667661229} & - \frac{27332418}{5667661229} & - \frac{128417656}{5667661229} & \frac{109633229}{5667661229} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Etapa 5.21.2

Simplifique $R_{2}$ .

Etapa 5.22

Perform the row operation $R_{1} = R_{1} + \frac{3}{4} R_{4}$ to make the entry at $1, 4$ a $0$ .

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Etapa 5.22.1

Perform the row operation $R_{1} = R_{1} + \frac{3}{4} R_{4}$ to make the entry at $1, 4$ a $0$ .

$[\begin{array}{c} 1 + \frac{3}{4} \cdot 0 & \frac{75}{44} + \frac{3}{4} \cdot 0 & - \frac{15}{11} + \frac{3}{4} \cdot 0 & - \frac{3}{4} + \frac{3}{4} \cdot 1 & 0 + \frac{3}{4} \cdot 0 & \frac{6431526969}{249377094076} + \frac{3}{4} (- \frac{29818171}{5667661229}) & \frac{13347167}{45341289832} + \frac{3}{4} \cdot \frac{21431433}{5667661229} & \frac{69437345}{45341289832} + \frac{3}{4} \cdot \frac{35092680}{5667661229} & - \frac{76448231}{45341289832} + \frac{3}{4} \cdot \frac{27413176}{5667661229} & - \frac{15823919}{22670644916} + \frac{3}{4} (- \frac{39162160}{5667661229}) \\ 0 & 1 & - \frac{376}{371} & 0 & 0 & \frac{14718065982}{2102702315959} & \frac{30952802595}{4205404631918} & \frac{240112235}{79347257206} & - \frac{25998754969}{4205404631918} & - \frac{797611705}{2102702315959} \\ 0 & 0 & 1 & 0 & 0 & - \frac{3615015}{5667661229} & \frac{38437093}{5667661229} & - \frac{27332418}{5667661229} & - \frac{128417656}{5667661229} & \frac{109633229}{5667661229} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Etapa 5.22.2

Simplifique $R_{1}$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & 0 & 0 & \frac{1892817}{86649442} & \frac{98635}{31508888} & \frac{194575}{31508888} & \frac{61175}{31508888} & - \frac{92641}{15754444} \\ 0 & 1 & - \frac{376}{371} & 0 & 0 & \frac{14718065982}{2102702315959} & \frac{30952802595}{4205404631918} & \frac{240112235}{79347257206} & - \frac{25998754969}{4205404631918} & - \frac{797611705}{2102702315959} \\ 0 & 0 & 1 & 0 & 0 & - \frac{3615015}{5667661229} & \frac{38437093}{5667661229} & - \frac{27332418}{5667661229} & - \frac{128417656}{5667661229} & \frac{109633229}{5667661229} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Etapa 5.23

Perform the row operation $R_{2} = R_{2} + \frac{376}{371} R_{3}$ to make the entry at $2, 3$ a $0$ .

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Etapa 5.23.1

Perform the row operation $R_{2} = R_{2} + \frac{376}{371} R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & 0 & 0 & \frac{1892817}{86649442} & \frac{98635}{31508888} & \frac{194575}{31508888} & \frac{61175}{31508888} & - \frac{92641}{15754444} \\ 0 + \frac{376}{371} \cdot 0 & 1 + \frac{376}{371} \cdot 0 & - \frac{376}{371} + \frac{376}{371} \cdot 1 & 0 + \frac{376}{371} \cdot 0 & 0 + \frac{376}{371} \cdot 0 & \frac{14718065982}{2102702315959} + \frac{376}{371} (- \frac{3615015}{5667661229}) & \frac{30952802595}{4205404631918} + \frac{376}{371} \cdot \frac{38437093}{5667661229} & \frac{240112235}{79347257206} + \frac{376}{371} (- \frac{27332418}{5667661229}) & - \frac{25998754969}{4205404631918} + \frac{376}{371} (- \frac{128417656}{5667661229}) & - \frac{797611705}{2102702315959} + \frac{376}{371} \cdot \frac{109633229}{5667661229} \\ 0 & 0 & 1 & 0 & 0 & - \frac{3615015}{5667661229} & \frac{38437093}{5667661229} & - \frac{27332418}{5667661229} & - \frac{128417656}{5667661229} & \frac{109633229}{5667661229} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Etapa 5.23.2

Simplifique $R_{2}$ .

$[\begin{array}{c} 1 & \frac{75}{44} & - \frac{15}{11} & 0 & 0 & \frac{1892817}{86649442} & \frac{98635}{31508888} & \frac{194575}{31508888} & \frac{61175}{31508888} & - \frac{92641}{15754444} \\ 0 & 1 & 0 & 0 & 0 & \frac{36007602}{5667661229} & \frac{161340961}{11335322458} & - \frac{21099811}{11335322458} & - \frac{330374211}{11335322458} & \frac{108960869}{5667661229} \\ 0 & 0 & 1 & 0 & 0 & - \frac{3615015}{5667661229} & \frac{38437093}{5667661229} & - \frac{27332418}{5667661229} & - \frac{128417656}{5667661229} & \frac{109633229}{5667661229} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Etapa 5.24

Perform the row operation $R_{1} = R_{1} + \frac{15}{11} R_{3}$ to make the entry at $1, 3$ a $0$ .

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Etapa 5.24.1

Perform the row operation $R_{1} = R_{1} + \frac{15}{11} R_{3}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 + \frac{15}{11} \cdot 0 & \frac{75}{44} + \frac{15}{11} \cdot 0 & - \frac{15}{11} + \frac{15}{11} \cdot 1 & 0 + \frac{15}{11} \cdot 0 & 0 + \frac{15}{11} \cdot 0 & \frac{1892817}{86649442} + \frac{15}{11} (- \frac{3615015}{5667661229}) & \frac{98635}{31508888} + \frac{15}{11} \cdot \frac{38437093}{5667661229} & \frac{194575}{31508888} + \frac{15}{11} (- \frac{27332418}{5667661229}) & \frac{61175}{31508888} + \frac{15}{11} (- \frac{128417656}{5667661229}) & - \frac{92641}{15754444} + \frac{15}{11} \cdot \frac{109633229}{5667661229} \\ 0 & 1 & 0 & 0 & 0 & \frac{36007602}{5667661229} & \frac{161340961}{11335322458} & - \frac{21099811}{11335322458} & - \frac{330374211}{11335322458} & \frac{108960869}{5667661229} \\ 0 & 0 & 1 & 0 & 0 & - \frac{3615015}{5667661229} & \frac{38437093}{5667661229} & - \frac{27332418}{5667661229} & - \frac{128417656}{5667661229} & \frac{109633229}{5667661229} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Etapa 5.24.2

Simplifique $R_{1}$ .

$[\begin{array}{c} 1 & \frac{75}{44} & 0 & 0 & 0 & \frac{2615313213}{124688547038} & \frac{6173744575}{498754188152} & - \frac{199962485}{498754188152} & - \frac{14441779645}{498754188152} & \frac{5111579351}{249377094076} \\ 0 & 1 & 0 & 0 & 0 & \frac{36007602}{5667661229} & \frac{161340961}{11335322458} & - \frac{21099811}{11335322458} & - \frac{330374211}{11335322458} & \frac{108960869}{5667661229} \\ 0 & 0 & 1 & 0 & 0 & - \frac{3615015}{5667661229} & \frac{38437093}{5667661229} & - \frac{27332418}{5667661229} & - \frac{128417656}{5667661229} & \frac{109633229}{5667661229} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Etapa 5.25

Perform the row operation $R_{1} = R_{1} - \frac{75}{44} R_{2}$ to make the entry at $1, 2$ a $0$ .

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Etapa 5.25.1

Perform the row operation $R_{1} = R_{1} - \frac{75}{44} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - \frac{75}{44} \cdot 0 & \frac{75}{44} - \frac{75}{44} \cdot 1 & 0 - \frac{75}{44} \cdot 0 & 0 - \frac{75}{44} \cdot 0 & 0 - \frac{75}{44} \cdot 0 & \frac{2615313213}{124688547038} - \frac{75}{44} \cdot \frac{36007602}{5667661229} & \frac{6173744575}{498754188152} - \frac{75}{44} \cdot \frac{161340961}{11335322458} & - \frac{199962485}{498754188152} - \frac{75}{44} (- \frac{21099811}{11335322458}) & - \frac{14441779645}{498754188152} - \frac{75}{44} (- \frac{330374211}{11335322458}) & \frac{5111579351}{249377094076} - \frac{75}{44} \cdot \frac{108960869}{5667661229} \\ 0 & 1 & 0 & 0 & 0 & \frac{36007602}{5667661229} & \frac{161340961}{11335322458} & - \frac{21099811}{11335322458} & - \frac{330374211}{11335322458} & \frac{108960869}{5667661229} \\ 0 & 0 & 1 & 0 & 0 & - \frac{3615015}{5667661229} & \frac{38437093}{5667661229} & - \frac{27332418}{5667661229} & - \frac{128417656}{5667661229} & \frac{109633229}{5667661229} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Etapa 5.25.2

Simplifique $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 0 & 0 & 0 & \frac{57501279}{5667661229} & - \frac{134700625}{11335322458} & \frac{31420985}{11335322458} & \frac{234915595}{11335322458} & - \frac{69556496}{5667661229} \\ 0 & 1 & 0 & 0 & 0 & \frac{36007602}{5667661229} & \frac{161340961}{11335322458} & - \frac{21099811}{11335322458} & - \frac{330374211}{11335322458} & \frac{108960869}{5667661229} \\ 0 & 0 & 1 & 0 & 0 & - \frac{3615015}{5667661229} & \frac{38437093}{5667661229} & - \frac{27332418}{5667661229} & - \frac{128417656}{5667661229} & \frac{109633229}{5667661229} \\ 0 & 0 & 0 & 1 & 0 & - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ 0 & 0 & 0 & 0 & 1 & - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$

Etapa 6

The right half of the reduced row echelon form is the inverse.

$[\begin{array}{c} \frac{57501279}{5667661229} & - \frac{134700625}{11335322458} & \frac{31420985}{11335322458} & \frac{234915595}{11335322458} & - \frac{69556496}{5667661229} \\ \frac{36007602}{5667661229} & \frac{161340961}{11335322458} & - \frac{21099811}{11335322458} & - \frac{330374211}{11335322458} & \frac{108960869}{5667661229} \\ - \frac{3615015}{5667661229} & \frac{38437093}{5667661229} & - \frac{27332418}{5667661229} & - \frac{128417656}{5667661229} & \frac{109633229}{5667661229} \\ - \frac{29818171}{5667661229} & \frac{21431433}{5667661229} & \frac{35092680}{5667661229} & \frac{27413176}{5667661229} & - \frac{39162160}{5667661229} \\ - \frac{69442340}{5667661229} & - \frac{13347167}{11335322458} & - \frac{69437345}{11335322458} & \frac{76448231}{11335322458} & \frac{15823919}{5667661229} \end{array}]$