Álgebra linear Exemplos

$[\begin{array}{c} 2 & 5 & 2 & 2 \\ 2 & 5 & 2 & 2 \\ 1 & 21 & 2 & 2 \\ 1 & 1 & 1 & 1 \end{array}] \cdot [\begin{array}{c} 5 & 7 & 7 & 10 \\ 3 & 3 & 2 & 1 \\ 3 & 47 & 58 & 5 \\ 4 & 4 & 10 & 10 \end{array}]$

Etapa 1

Multiplique $[\begin{array}{c} 2 & 5 & 2 & 2 \\ 2 & 5 & 2 & 2 \\ 1 & 21 & 2 & 2 \\ 1 & 1 & 1 & 1 \end{array}] [\begin{array}{c} 5 & 7 & 7 & 10 \\ 3 & 3 & 2 & 1 \\ 3 & 47 & 58 & 5 \\ 4 & 4 & 10 & 10 \end{array}]$ .

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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 $4 \times 4$ and the second matrix is $4 \times 4$ .

Etapa 1.2

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

$[\begin{array}{c} 2 \cdot 5 + 5 \cdot 3 + 2 \cdot 3 + 2 \cdot 4 & 2 \cdot 7 + 5 \cdot 3 + 2 \cdot 47 + 2 \cdot 4 & 2 \cdot 7 + 5 \cdot 2 + 2 \cdot 58 + 2 \cdot 10 & 2 \cdot 10 + 5 \cdot 1 + 2 \cdot 5 + 2 \cdot 10 \\ 2 \cdot 5 + 5 \cdot 3 + 2 \cdot 3 + 2 \cdot 4 & 2 \cdot 7 + 5 \cdot 3 + 2 \cdot 47 + 2 \cdot 4 & 2 \cdot 7 + 5 \cdot 2 + 2 \cdot 58 + 2 \cdot 10 & 2 \cdot 10 + 5 \cdot 1 + 2 \cdot 5 + 2 \cdot 10 \\ 1 \cdot 5 + 21 \cdot 3 + 2 \cdot 3 + 2 \cdot 4 & 1 \cdot 7 + 21 \cdot 3 + 2 \cdot 47 + 2 \cdot 4 & 1 \cdot 7 + 21 \cdot 2 + 2 \cdot 58 + 2 \cdot 10 & 1 \cdot 10 + 21 \cdot 1 + 2 \cdot 5 + 2 \cdot 10 \\ 1 \cdot 5 + 1 \cdot 3 + 1 \cdot 3 + 1 \cdot 4 & 1 \cdot 7 + 1 \cdot 3 + 1 \cdot 47 + 1 \cdot 4 & 1 \cdot 7 + 1 \cdot 2 + 1 \cdot 58 + 1 \cdot 10 & 1 \cdot 10 + 1 \cdot 1 + 1 \cdot 5 + 1 \cdot 10 \end{array}]$

Etapa 1.3

Simplifique cada elemento da matriz multiplicando todas as expressões.

$[\begin{array}{c} 39 & 131 & 160 & 55 \\ 39 & 131 & 160 & 55 \\ 82 & 172 & 185 & 61 \\ 15 & 61 & 77 & 26 \end{array}]$

Etapa 2

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

Consider the corresponding sign chart.

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

Etapa 2.2

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

Etapa 2.3

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

$| \begin{array}{c} 131 & 160 & 55 \\ 172 & 185 & 61 \\ 61 & 77 & 26 \end{array} |$

Etapa 2.4

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

$39 | \begin{array}{c} 131 & 160 & 55 \\ 172 & 185 & 61 \\ 61 & 77 & 26 \end{array} |$

Etapa 2.5

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

$| \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} |$

Etapa 2.6

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

$- 131 | \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} |$

Etapa 2.7

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

$| \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} |$

Etapa 2.8

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

$160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} |$

Etapa 2.9

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

$| \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 2.10

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

$- 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 2.11

Add the terms together.

$39 | \begin{array}{c} 131 & 160 & 55 \\ 172 & 185 & 61 \\ 61 & 77 & 26 \end{array} | - 131 | \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} | + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 3

Avalie $| \begin{array}{c} 131 & 160 & 55 \\ 172 & 185 & 61 \\ 61 & 77 & 26 \end{array} |$ .

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Etapa 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 3.1.1

Consider the corresponding sign chart.

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

Etapa 3.1.2

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

Etapa 3.1.3

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

$| \begin{array}{c} 185 & 61 \\ 77 & 26 \end{array} |$

Etapa 3.1.4

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

$131 | \begin{array}{c} 185 & 61 \\ 77 & 26 \end{array} |$

Etapa 3.1.5

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

$| \begin{array}{c} 172 & 61 \\ 61 & 26 \end{array} |$

Etapa 3.1.6

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

$- 160 | \begin{array}{c} 172 & 61 \\ 61 & 26 \end{array} |$

Etapa 3.1.7

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

$| \begin{array}{c} 172 & 185 \\ 61 & 77 \end{array} |$

Etapa 3.1.8

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

$55 | \begin{array}{c} 172 & 185 \\ 61 & 77 \end{array} |$

Etapa 3.1.9

Add the terms together.

$39 (131 | \begin{array}{c} 185 & 61 \\ 77 & 26 \end{array} | - 160 | \begin{array}{c} 172 & 61 \\ 61 & 26 \end{array} | + 55 | \begin{array}{c} 172 & 185 \\ 61 & 77 \end{array} |) - 131 | \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} | + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 3.2

Avalie $| \begin{array}{c} 185 & 61 \\ 77 & 26 \end{array} |$ .

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Etapa 3.2.1

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

$39 (131 (185 \cdot 26 - 77 \cdot 61) - 160 | \begin{array}{c} 172 & 61 \\ 61 & 26 \end{array} | + 55 | \begin{array}{c} 172 & 185 \\ 61 & 77 \end{array} |) - 131 | \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} | + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 3.2.2

Simplifique o determinante.

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Etapa 3.2.2.1

Simplifique cada termo.

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Etapa 3.2.2.1.1

Multiplique $185$ por $26$ .

$39 (131 (4810 - 77 \cdot 61) - 160 | \begin{array}{c} 172 & 61 \\ 61 & 26 \end{array} | + 55 | \begin{array}{c} 172 & 185 \\ 61 & 77 \end{array} |) - 131 | \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} | + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 3.2.2.1.2

Multiplique $- 77$ por $61$ .

$39 (131 (4810 - 4697) - 160 | \begin{array}{c} 172 & 61 \\ 61 & 26 \end{array} | + 55 | \begin{array}{c} 172 & 185 \\ 61 & 77 \end{array} |) - 131 | \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} | + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 3.2.2.2

Subtraia $4697$ de $4810$ .

$39 (131 \cdot 113 - 160 | \begin{array}{c} 172 & 61 \\ 61 & 26 \end{array} | + 55 | \begin{array}{c} 172 & 185 \\ 61 & 77 \end{array} |) - 131 | \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} | + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 3.3

Avalie $| \begin{array}{c} 172 & 61 \\ 61 & 26 \end{array} |$ .

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Etapa 3.3.1

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

$39 (131 \cdot 113 - 160 (172 \cdot 26 - 61 \cdot 61) + 55 | \begin{array}{c} 172 & 185 \\ 61 & 77 \end{array} |) - 131 | \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} | + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 3.3.2

Simplifique o determinante.

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Etapa 3.3.2.1

Simplifique cada termo.

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Etapa 3.3.2.1.1

Multiplique $172$ por $26$ .

$39 (131 \cdot 113 - 160 (4472 - 61 \cdot 61) + 55 | \begin{array}{c} 172 & 185 \\ 61 & 77 \end{array} |) - 131 | \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} | + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 3.3.2.1.2

Multiplique $- 61$ por $61$ .

$39 (131 \cdot 113 - 160 (4472 - 3721) + 55 | \begin{array}{c} 172 & 185 \\ 61 & 77 \end{array} |) - 131 | \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} | + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 3.3.2.2

Subtraia $3721$ de $4472$ .

$39 (131 \cdot 113 - 160 \cdot 751 + 55 | \begin{array}{c} 172 & 185 \\ 61 & 77 \end{array} |) - 131 | \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} | + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 3.4

Avalie $| \begin{array}{c} 172 & 185 \\ 61 & 77 \end{array} |$ .

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Etapa 3.4.1

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

$39 (131 \cdot 113 - 160 \cdot 751 + 55 (172 \cdot 77 - 61 \cdot 185)) - 131 | \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} | + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 3.4.2

Simplifique o determinante.

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Etapa 3.4.2.1

Simplifique cada termo.

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Etapa 3.4.2.1.1

Multiplique $172$ por $77$ .

$39 (131 \cdot 113 - 160 \cdot 751 + 55 (13244 - 61 \cdot 185)) - 131 | \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} | + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 3.4.2.1.2

Multiplique $- 61$ por $185$ .

$39 (131 \cdot 113 - 160 \cdot 751 + 55 (13244 - 11285)) - 131 | \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} | + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 3.4.2.2

Subtraia $11285$ de $13244$ .

$39 (131 \cdot 113 - 160 \cdot 751 + 55 \cdot 1959) - 131 | \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} | + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 3.5

Simplifique o determinante.

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Etapa 3.5.1

Simplifique cada termo.

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Etapa 3.5.1.1

Multiplique $131$ por $113$ .

$39 (14803 - 160 \cdot 751 + 55 \cdot 1959) - 131 | \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} | + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 3.5.1.2

Multiplique $- 160$ por $751$ .

$39 (14803 - 120160 + 55 \cdot 1959) - 131 | \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} | + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 3.5.1.3

Multiplique $55$ por $1959$ .

$39 (14803 - 120160 + 107745) - 131 | \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} | + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 3.5.2

Subtraia $120160$ de $14803$ .

$39 (- 105357 + 107745) - 131 | \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} | + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 3.5.3

Some $- 105357$ e $107745$ .

$39 \cdot 2388 - 131 | \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} | + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 4

Avalie $| \begin{array}{c} 39 & 160 & 55 \\ 82 & 185 & 61 \\ 15 & 77 & 26 \end{array} |$ .

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Etapa 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 4.1.1

Consider the corresponding sign chart.

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

Etapa 4.1.2

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

Etapa 4.1.3

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

$| \begin{array}{c} 185 & 61 \\ 77 & 26 \end{array} |$

Etapa 4.1.4

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

$39 | \begin{array}{c} 185 & 61 \\ 77 & 26 \end{array} |$

Etapa 4.1.5

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

$| \begin{array}{c} 82 & 61 \\ 15 & 26 \end{array} |$

Etapa 4.1.6

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

$- 160 | \begin{array}{c} 82 & 61 \\ 15 & 26 \end{array} |$

Etapa 4.1.7

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

$| \begin{array}{c} 82 & 185 \\ 15 & 77 \end{array} |$

Etapa 4.1.8

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

$55 | \begin{array}{c} 82 & 185 \\ 15 & 77 \end{array} |$

Etapa 4.1.9

Add the terms together.

$39 \cdot 2388 - 131 (39 | \begin{array}{c} 185 & 61 \\ 77 & 26 \end{array} | - 160 | \begin{array}{c} 82 & 61 \\ 15 & 26 \end{array} | + 55 | \begin{array}{c} 82 & 185 \\ 15 & 77 \end{array} |) + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 4.2

Avalie $| \begin{array}{c} 185 & 61 \\ 77 & 26 \end{array} |$ .

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Etapa 4.2.1

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

$39 \cdot 2388 - 131 (39 (185 \cdot 26 - 77 \cdot 61) - 160 | \begin{array}{c} 82 & 61 \\ 15 & 26 \end{array} | + 55 | \begin{array}{c} 82 & 185 \\ 15 & 77 \end{array} |) + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 4.2.2

Simplifique o determinante.

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Etapa 4.2.2.1

Simplifique cada termo.

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Etapa 4.2.2.1.1

Multiplique $185$ por $26$ .

$39 \cdot 2388 - 131 (39 (4810 - 77 \cdot 61) - 160 | \begin{array}{c} 82 & 61 \\ 15 & 26 \end{array} | + 55 | \begin{array}{c} 82 & 185 \\ 15 & 77 \end{array} |) + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 4.2.2.1.2

Multiplique $- 77$ por $61$ .

$39 \cdot 2388 - 131 (39 (4810 - 4697) - 160 | \begin{array}{c} 82 & 61 \\ 15 & 26 \end{array} | + 55 | \begin{array}{c} 82 & 185 \\ 15 & 77 \end{array} |) + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 4.2.2.2

Subtraia $4697$ de $4810$ .

$39 \cdot 2388 - 131 (39 \cdot 113 - 160 | \begin{array}{c} 82 & 61 \\ 15 & 26 \end{array} | + 55 | \begin{array}{c} 82 & 185 \\ 15 & 77 \end{array} |) + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 4.3

Avalie $| \begin{array}{c} 82 & 61 \\ 15 & 26 \end{array} |$ .

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Etapa 4.3.1

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

$39 \cdot 2388 - 131 (39 \cdot 113 - 160 (82 \cdot 26 - 15 \cdot 61) + 55 | \begin{array}{c} 82 & 185 \\ 15 & 77 \end{array} |) + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 4.3.2

Simplifique o determinante.

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Etapa 4.3.2.1

Simplifique cada termo.

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Etapa 4.3.2.1.1

Multiplique $82$ por $26$ .

$39 \cdot 2388 - 131 (39 \cdot 113 - 160 (2132 - 15 \cdot 61) + 55 | \begin{array}{c} 82 & 185 \\ 15 & 77 \end{array} |) + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 4.3.2.1.2

Multiplique $- 15$ por $61$ .

$39 \cdot 2388 - 131 (39 \cdot 113 - 160 (2132 - 915) + 55 | \begin{array}{c} 82 & 185 \\ 15 & 77 \end{array} |) + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 4.3.2.2

Subtraia $915$ de $2132$ .

$39 \cdot 2388 - 131 (39 \cdot 113 - 160 \cdot 1217 + 55 | \begin{array}{c} 82 & 185 \\ 15 & 77 \end{array} |) + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 4.4

Avalie $| \begin{array}{c} 82 & 185 \\ 15 & 77 \end{array} |$ .

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Etapa 4.4.1

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

$39 \cdot 2388 - 131 (39 \cdot 113 - 160 \cdot 1217 + 55 (82 \cdot 77 - 15 \cdot 185)) + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 4.4.2

Simplifique o determinante.

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Etapa 4.4.2.1

Simplifique cada termo.

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Etapa 4.4.2.1.1

Multiplique $82$ por $77$ .

$39 \cdot 2388 - 131 (39 \cdot 113 - 160 \cdot 1217 + 55 (6314 - 15 \cdot 185)) + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 4.4.2.1.2

Multiplique $- 15$ por $185$ .

$39 \cdot 2388 - 131 (39 \cdot 113 - 160 \cdot 1217 + 55 (6314 - 2775)) + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 4.4.2.2

Subtraia $2775$ de $6314$ .

$39 \cdot 2388 - 131 (39 \cdot 113 - 160 \cdot 1217 + 55 \cdot 3539) + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 4.5

Simplifique o determinante.

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Etapa 4.5.1

Simplifique cada termo.

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Etapa 4.5.1.1

Multiplique $39$ por $113$ .

$39 \cdot 2388 - 131 (4407 - 160 \cdot 1217 + 55 \cdot 3539) + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 4.5.1.2

Multiplique $- 160$ por $1217$ .

$39 \cdot 2388 - 131 (4407 - 194720 + 55 \cdot 3539) + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 4.5.1.3

Multiplique $55$ por $3539$ .

$39 \cdot 2388 - 131 (4407 - 194720 + 194645) + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 4.5.2

Subtraia $194720$ de $4407$ .

$39 \cdot 2388 - 131 (- 190313 + 194645) + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 4.5.3

Some $- 190313$ e $194645$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 | \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} | - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 5

Avalie $| \begin{array}{c} 39 & 131 & 55 \\ 82 & 172 & 61 \\ 15 & 61 & 26 \end{array} |$ .

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Etapa 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 5.1.1

Consider the corresponding sign chart.

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

Etapa 5.1.2

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

Etapa 5.1.3

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

$| \begin{array}{c} 172 & 61 \\ 61 & 26 \end{array} |$

Etapa 5.1.4

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

$39 | \begin{array}{c} 172 & 61 \\ 61 & 26 \end{array} |$

Etapa 5.1.5

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

$| \begin{array}{c} 82 & 61 \\ 15 & 26 \end{array} |$

Etapa 5.1.6

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

$- 131 | \begin{array}{c} 82 & 61 \\ 15 & 26 \end{array} |$

Etapa 5.1.7

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

$| \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |$

Etapa 5.1.8

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

$55 | \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |$

Etapa 5.1.9

Add the terms together.

$39 \cdot 2388 - 131 \cdot 4332 + 160 (39 | \begin{array}{c} 172 & 61 \\ 61 & 26 \end{array} | - 131 | \begin{array}{c} 82 & 61 \\ 15 & 26 \end{array} | + 55 | \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |) - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 5.2

Avalie $| \begin{array}{c} 172 & 61 \\ 61 & 26 \end{array} |$ .

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Etapa 5.2.1

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

$39 \cdot 2388 - 131 \cdot 4332 + 160 (39 (172 \cdot 26 - 61 \cdot 61) - 131 | \begin{array}{c} 82 & 61 \\ 15 & 26 \end{array} | + 55 | \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |) - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 5.2.2

Simplifique o determinante.

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Etapa 5.2.2.1

Simplifique cada termo.

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Etapa 5.2.2.1.1

Multiplique $172$ por $26$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 (39 (4472 - 61 \cdot 61) - 131 | \begin{array}{c} 82 & 61 \\ 15 & 26 \end{array} | + 55 | \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |) - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 5.2.2.1.2

Multiplique $- 61$ por $61$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 (39 (4472 - 3721) - 131 | \begin{array}{c} 82 & 61 \\ 15 & 26 \end{array} | + 55 | \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |) - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 5.2.2.2

Subtraia $3721$ de $4472$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 (39 \cdot 751 - 131 | \begin{array}{c} 82 & 61 \\ 15 & 26 \end{array} | + 55 | \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |) - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 5.3

Avalie $| \begin{array}{c} 82 & 61 \\ 15 & 26 \end{array} |$ .

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Etapa 5.3.1

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

$39 \cdot 2388 - 131 \cdot 4332 + 160 (39 \cdot 751 - 131 (82 \cdot 26 - 15 \cdot 61) + 55 | \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |) - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 5.3.2

Simplifique o determinante.

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Etapa 5.3.2.1

Simplifique cada termo.

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Etapa 5.3.2.1.1

Multiplique $82$ por $26$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 (39 \cdot 751 - 131 (2132 - 15 \cdot 61) + 55 | \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |) - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 5.3.2.1.2

Multiplique $- 15$ por $61$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 (39 \cdot 751 - 131 (2132 - 915) + 55 | \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |) - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 5.3.2.2

Subtraia $915$ de $2132$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 (39 \cdot 751 - 131 \cdot 1217 + 55 | \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |) - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 5.4

Avalie $| \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |$ .

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Etapa 5.4.1

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

$39 \cdot 2388 - 131 \cdot 4332 + 160 (39 \cdot 751 - 131 \cdot 1217 + 55 (82 \cdot 61 - 15 \cdot 172)) - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 5.4.2

Simplifique o determinante.

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Etapa 5.4.2.1

Simplifique cada termo.

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Etapa 5.4.2.1.1

Multiplique $82$ por $61$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 (39 \cdot 751 - 131 \cdot 1217 + 55 (5002 - 15 \cdot 172)) - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 5.4.2.1.2

Multiplique $- 15$ por $172$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 (39 \cdot 751 - 131 \cdot 1217 + 55 (5002 - 2580)) - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 5.4.2.2

Subtraia $2580$ de $5002$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 (39 \cdot 751 - 131 \cdot 1217 + 55 \cdot 2422) - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 5.5

Simplifique o determinante.

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Etapa 5.5.1

Simplifique cada termo.

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Etapa 5.5.1.1

Multiplique $39$ por $751$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 (29289 - 131 \cdot 1217 + 55 \cdot 2422) - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 5.5.1.2

Multiplique $- 131$ por $1217$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 (29289 - 159427 + 55 \cdot 2422) - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 5.5.1.3

Multiplique $55$ por $2422$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 (29289 - 159427 + 133210) - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 5.5.2

Subtraia $159427$ de $29289$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 (- 130138 + 133210) - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 5.5.3

Some $- 130138$ e $133210$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 \cdot 3072 - 55 | \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$

Etapa 6

Avalie $| \begin{array}{c} 39 & 131 & 160 \\ 82 & 172 & 185 \\ 15 & 61 & 77 \end{array} |$ .

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Etapa 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 6.1.1

Consider the corresponding sign chart.

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

Etapa 6.1.2

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

Etapa 6.1.3

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

$| \begin{array}{c} 172 & 185 \\ 61 & 77 \end{array} |$

Etapa 6.1.4

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

$39 | \begin{array}{c} 172 & 185 \\ 61 & 77 \end{array} |$

Etapa 6.1.5

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

$| \begin{array}{c} 82 & 185 \\ 15 & 77 \end{array} |$

Etapa 6.1.6

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

$- 131 | \begin{array}{c} 82 & 185 \\ 15 & 77 \end{array} |$

Etapa 6.1.7

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

$| \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |$

Etapa 6.1.8

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

$160 | \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |$

Etapa 6.1.9

Add the terms together.

$39 \cdot 2388 - 131 \cdot 4332 + 160 \cdot 3072 - 55 (39 | \begin{array}{c} 172 & 185 \\ 61 & 77 \end{array} | - 131 | \begin{array}{c} 82 & 185 \\ 15 & 77 \end{array} | + 160 | \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |)$

Etapa 6.2

Avalie $| \begin{array}{c} 172 & 185 \\ 61 & 77 \end{array} |$ .

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Etapa 6.2.1

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

$39 \cdot 2388 - 131 \cdot 4332 + 160 \cdot 3072 - 55 (39 (172 \cdot 77 - 61 \cdot 185) - 131 | \begin{array}{c} 82 & 185 \\ 15 & 77 \end{array} | + 160 | \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |)$

Etapa 6.2.2

Simplifique o determinante.

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Etapa 6.2.2.1

Simplifique cada termo.

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Etapa 6.2.2.1.1

Multiplique $172$ por $77$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 \cdot 3072 - 55 (39 (13244 - 61 \cdot 185) - 131 | \begin{array}{c} 82 & 185 \\ 15 & 77 \end{array} | + 160 | \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |)$

Etapa 6.2.2.1.2

Multiplique $- 61$ por $185$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 \cdot 3072 - 55 (39 (13244 - 11285) - 131 | \begin{array}{c} 82 & 185 \\ 15 & 77 \end{array} | + 160 | \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |)$

Etapa 6.2.2.2

Subtraia $11285$ de $13244$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 \cdot 3072 - 55 (39 \cdot 1959 - 131 | \begin{array}{c} 82 & 185 \\ 15 & 77 \end{array} | + 160 | \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |)$

Etapa 6.3

Avalie $| \begin{array}{c} 82 & 185 \\ 15 & 77 \end{array} |$ .

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Etapa 6.3.1

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

$39 \cdot 2388 - 131 \cdot 4332 + 160 \cdot 3072 - 55 (39 \cdot 1959 - 131 (82 \cdot 77 - 15 \cdot 185) + 160 | \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |)$

Etapa 6.3.2

Simplifique o determinante.

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Etapa 6.3.2.1

Simplifique cada termo.

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Etapa 6.3.2.1.1

Multiplique $82$ por $77$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 \cdot 3072 - 55 (39 \cdot 1959 - 131 (6314 - 15 \cdot 185) + 160 | \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |)$

Etapa 6.3.2.1.2

Multiplique $- 15$ por $185$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 \cdot 3072 - 55 (39 \cdot 1959 - 131 (6314 - 2775) + 160 | \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |)$

Etapa 6.3.2.2

Subtraia $2775$ de $6314$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 \cdot 3072 - 55 (39 \cdot 1959 - 131 \cdot 3539 + 160 | \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |)$

Etapa 6.4

Avalie $| \begin{array}{c} 82 & 172 \\ 15 & 61 \end{array} |$ .

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Etapa 6.4.1

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

$39 \cdot 2388 - 131 \cdot 4332 + 160 \cdot 3072 - 55 (39 \cdot 1959 - 131 \cdot 3539 + 160 (82 \cdot 61 - 15 \cdot 172))$

Etapa 6.4.2

Simplifique o determinante.

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Etapa 6.4.2.1

Simplifique cada termo.

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Etapa 6.4.2.1.1

Multiplique $82$ por $61$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 \cdot 3072 - 55 (39 \cdot 1959 - 131 \cdot 3539 + 160 (5002 - 15 \cdot 172))$

Etapa 6.4.2.1.2

Multiplique $- 15$ por $172$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 \cdot 3072 - 55 (39 \cdot 1959 - 131 \cdot 3539 + 160 (5002 - 2580))$

Etapa 6.4.2.2

Subtraia $2580$ de $5002$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 \cdot 3072 - 55 (39 \cdot 1959 - 131 \cdot 3539 + 160 \cdot 2422)$

Etapa 6.5

Simplifique o determinante.

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Etapa 6.5.1

Simplifique cada termo.

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Etapa 6.5.1.1

Multiplique $39$ por $1959$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 \cdot 3072 - 55 (76401 - 131 \cdot 3539 + 160 \cdot 2422)$

Etapa 6.5.1.2

Multiplique $- 131$ por $3539$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 \cdot 3072 - 55 (76401 - 463609 + 160 \cdot 2422)$

Etapa 6.5.1.3

Multiplique $160$ por $2422$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 \cdot 3072 - 55 (76401 - 463609 + 387520)$

Etapa 6.5.2

Subtraia $463609$ de $76401$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 \cdot 3072 - 55 (- 387208 + 387520)$

Etapa 6.5.3

Some $- 387208$ e $387520$ .

$39 \cdot 2388 - 131 \cdot 4332 + 160 \cdot 3072 - 55 \cdot 312$

Etapa 7

Simplifique o determinante.

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Etapa 7.1

Simplifique cada termo.

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Etapa 7.1.1

Multiplique $39$ por $2388$ .

$93132 - 131 \cdot 4332 + 160 \cdot 3072 - 55 \cdot 312$

Etapa 7.1.2

Multiplique $- 131$ por $4332$ .

$93132 - 567492 + 160 \cdot 3072 - 55 \cdot 312$

Etapa 7.1.3

Multiplique $160$ por $3072$ .

$93132 - 567492 + 491520 - 55 \cdot 312$

Etapa 7.1.4

Multiplique $- 55$ por $312$ .

$93132 - 567492 + 491520 - 17160$

Etapa 7.2

Subtraia $567492$ de $93132$ .

$- 474360 + 491520 - 17160$

Etapa 7.3

Some $- 474360$ e $491520$ .

$17160 - 17160$

Etapa 7.4

Subtraia $17160$ de $17160$ .

$0$