Álgebra linear Exemplos

$[\begin{array}{c} 7 & 2.12 & - 3.25 & 5.2 \\ 4 & 3 & 5 & - 2 \\ 1.23 & 5.21 & - 4.03 & 7.2 \\ 4.2 & 12.06 & - 3.085 & 4.74 \end{array}] \cdot 4 - 3.085$

Etapa 1

Simplifique cada termo.

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Etapa 1.1

Mova $4$ para a esquerda de $[\begin{array}{c} 7 & 2.12 & - 3.25 & 5.2 \\ 4 & 3 & 5 & - 2 \\ 1.23 & 5.21 & - 4.03 & 7.2 \\ 4.2 & 12.06 & - 3.085 & 4.74 \end{array}]$ .

$4 \cdot [\begin{array}{c} 7 & 2.12 & - 3.25 & 5.2 \\ 4 & 3 & 5 & - 2 \\ 1.23 & 5.21 & - 4.03 & 7.2 \\ 4.2 & 12.06 & - 3.085 & 4.74 \end{array}] - 3.085$

Etapa 1.2

Multiplique $4$ por cada elemento da matriz.

$[\begin{array}{c} 4 \cdot 7 & 4 \cdot 2.12 & 4 \cdot - 3.25 & 4 \cdot 5.2 \\ 4 \cdot 4 & 4 \cdot 3 & 4 \cdot 5 & 4 \cdot - 2 \\ 4 \cdot 1.23 & 4 \cdot 5.21 & 4 \cdot - 4.03 & 4 \cdot 7.2 \\ 4 \cdot 4.2 & 4 \cdot 12.06 & 4 \cdot - 3.085 & 4 \cdot 4.74 \end{array}] - 3.085$

Etapa 1.3

Simplifique cada elemento da matriz.

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Etapa 1.3.1

Multiplique $4$ por $7$ .

$[\begin{array}{c} 28 & 4 \cdot 2.12 & 4 \cdot - 3.25 & 4 \cdot 5.2 \\ 4 \cdot 4 & 4 \cdot 3 & 4 \cdot 5 & 4 \cdot - 2 \\ 4 \cdot 1.23 & 4 \cdot 5.21 & 4 \cdot - 4.03 & 4 \cdot 7.2 \\ 4 \cdot 4.2 & 4 \cdot 12.06 & 4 \cdot - 3.085 & 4 \cdot 4.74 \end{array}] - 3.085$

Etapa 1.3.2

Multiplique $4$ por $2.12$ .

$[\begin{array}{c} 28 & 8.48 & 4 \cdot - 3.25 & 4 \cdot 5.2 \\ 4 \cdot 4 & 4 \cdot 3 & 4 \cdot 5 & 4 \cdot - 2 \\ 4 \cdot 1.23 & 4 \cdot 5.21 & 4 \cdot - 4.03 & 4 \cdot 7.2 \\ 4 \cdot 4.2 & 4 \cdot 12.06 & 4 \cdot - 3.085 & 4 \cdot 4.74 \end{array}] - 3.085$

Etapa 1.3.3

Multiplique $4$ por $- 3.25$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 4 \cdot 5.2 \\ 4 \cdot 4 & 4 \cdot 3 & 4 \cdot 5 & 4 \cdot - 2 \\ 4 \cdot 1.23 & 4 \cdot 5.21 & 4 \cdot - 4.03 & 4 \cdot 7.2 \\ 4 \cdot 4.2 & 4 \cdot 12.06 & 4 \cdot - 3.085 & 4 \cdot 4.74 \end{array}] - 3.085$

Etapa 1.3.4

Multiplique $4$ por $5.2$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 4 \cdot 4 & 4 \cdot 3 & 4 \cdot 5 & 4 \cdot - 2 \\ 4 \cdot 1.23 & 4 \cdot 5.21 & 4 \cdot - 4.03 & 4 \cdot 7.2 \\ 4 \cdot 4.2 & 4 \cdot 12.06 & 4 \cdot - 3.085 & 4 \cdot 4.74 \end{array}] - 3.085$

Etapa 1.3.5

Multiplique $4$ por $4$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 4 \cdot 3 & 4 \cdot 5 & 4 \cdot - 2 \\ 4 \cdot 1.23 & 4 \cdot 5.21 & 4 \cdot - 4.03 & 4 \cdot 7.2 \\ 4 \cdot 4.2 & 4 \cdot 12.06 & 4 \cdot - 3.085 & 4 \cdot 4.74 \end{array}] - 3.085$

Etapa 1.3.6

Multiplique $4$ por $3$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 4 \cdot 5 & 4 \cdot - 2 \\ 4 \cdot 1.23 & 4 \cdot 5.21 & 4 \cdot - 4.03 & 4 \cdot 7.2 \\ 4 \cdot 4.2 & 4 \cdot 12.06 & 4 \cdot - 3.085 & 4 \cdot 4.74 \end{array}] - 3.085$

Etapa 1.3.7

Multiplique $4$ por $5$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & 4 \cdot - 2 \\ 4 \cdot 1.23 & 4 \cdot 5.21 & 4 \cdot - 4.03 & 4 \cdot 7.2 \\ 4 \cdot 4.2 & 4 \cdot 12.06 & 4 \cdot - 3.085 & 4 \cdot 4.74 \end{array}] - 3.085$

Etapa 1.3.8

Multiplique $4$ por $- 2$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4 \cdot 1.23 & 4 \cdot 5.21 & 4 \cdot - 4.03 & 4 \cdot 7.2 \\ 4 \cdot 4.2 & 4 \cdot 12.06 & 4 \cdot - 3.085 & 4 \cdot 4.74 \end{array}] - 3.085$

Etapa 1.3.9

Multiplique $4$ por $1.23$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 4 \cdot 5.21 & 4 \cdot - 4.03 & 4 \cdot 7.2 \\ 4 \cdot 4.2 & 4 \cdot 12.06 & 4 \cdot - 3.085 & 4 \cdot 4.74 \end{array}] - 3.085$

Etapa 1.3.10

Multiplique $4$ por $5.21$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & 4 \cdot - 4.03 & 4 \cdot 7.2 \\ 4 \cdot 4.2 & 4 \cdot 12.06 & 4 \cdot - 3.085 & 4 \cdot 4.74 \end{array}] - 3.085$

Etapa 1.3.11

Multiplique $4$ por $- 4.03$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 4 \cdot 7.2 \\ 4 \cdot 4.2 & 4 \cdot 12.06 & 4 \cdot - 3.085 & 4 \cdot 4.74 \end{array}] - 3.085$

Etapa 1.3.12

Multiplique $4$ por $7.2$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 4 \cdot 4.2 & 4 \cdot 12.06 & 4 \cdot - 3.085 & 4 \cdot 4.74 \end{array}] - 3.085$

Etapa 1.3.13

Multiplique $4$ por $4.2$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 4 \cdot 12.06 & 4 \cdot - 3.085 & 4 \cdot 4.74 \end{array}] - 3.085$

Etapa 1.3.14

Multiplique $4$ por $12.06$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & 4 \cdot - 3.085 & 4 \cdot 4.74 \end{array}] - 3.085$

Etapa 1.3.15

Multiplique $4$ por $- 3.085$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 4 \cdot 4.74 \end{array}] - 3.085$

Etapa 1.3.16

Multiplique $4$ por $4.74$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 18.96 \end{array}] - 3.085$

Etapa 2

Adding $- 3.085$ to a $4 \times 4$ square matrix is the same as adding $- 3.085$ times the $4 \times 4$ identity matrix.

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 18.96 \end{array}] - 3.085 [\begin{array}{c} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}]$

Etapa 3

Multiplique $- 3.085$ por cada elemento da matriz.

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 18.96 \end{array}] + [\begin{array}{c} - 3.085 \cdot 1 & - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 1 & - 3.085 \cdot 0 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 \end{array}]$

Etapa 4

Simplifique cada elemento da matriz.

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Etapa 4.1

Multiplique $- 3.085$ por $1$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 18.96 \end{array}] + [\begin{array}{c} - 3.085 & - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 1 & - 3.085 \cdot 0 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 \end{array}]$

Etapa 4.2

Multiplique $- 3.085$ por $0$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 18.96 \end{array}] + [\begin{array}{c} - 3.085 & 0 & - 3.085 \cdot 0 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 1 & - 3.085 \cdot 0 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 \end{array}]$

Etapa 4.3

Multiplique $- 3.085$ por $0$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 18.96 \end{array}] + [\begin{array}{c} - 3.085 & 0 & 0 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 1 & - 3.085 \cdot 0 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 \end{array}]$

Etapa 4.4

Multiplique $- 3.085$ por $0$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 18.96 \end{array}] + [\begin{array}{c} - 3.085 & 0 & 0 & 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 1 & - 3.085 \cdot 0 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 \end{array}]$

Etapa 4.5

Multiplique $- 3.085$ por $0$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 18.96 \end{array}] + [\begin{array}{c} - 3.085 & 0 & 0 & 0 \\ 0 & - 3.085 \cdot 1 & - 3.085 \cdot 0 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 \end{array}]$

Etapa 4.6

Multiplique $- 3.085$ por $1$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 18.96 \end{array}] + [\begin{array}{c} - 3.085 & 0 & 0 & 0 \\ 0 & - 3.085 & - 3.085 \cdot 0 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 \end{array}]$

Etapa 4.7

Multiplique $- 3.085$ por $0$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 18.96 \end{array}] + [\begin{array}{c} - 3.085 & 0 & 0 & 0 \\ 0 & - 3.085 & 0 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 \end{array}]$

Etapa 4.8

Multiplique $- 3.085$ por $0$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 18.96 \end{array}] + [\begin{array}{c} - 3.085 & 0 & 0 & 0 \\ 0 & - 3.085 & 0 & 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 \end{array}]$

Etapa 4.9

Multiplique $- 3.085$ por $0$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 18.96 \end{array}] + [\begin{array}{c} - 3.085 & 0 & 0 & 0 \\ 0 & - 3.085 & 0 & 0 \\ 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 \end{array}]$

Etapa 4.10

Multiplique $- 3.085$ por $0$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 18.96 \end{array}] + [\begin{array}{c} - 3.085 & 0 & 0 & 0 \\ 0 & - 3.085 & 0 & 0 \\ 0 & 0 & - 3.085 \cdot 1 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 \end{array}]$

Etapa 4.11

Multiplique $- 3.085$ por $1$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 18.96 \end{array}] + [\begin{array}{c} - 3.085 & 0 & 0 & 0 \\ 0 & - 3.085 & 0 & 0 \\ 0 & 0 & - 3.085 & - 3.085 \cdot 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 \end{array}]$

Etapa 4.12

Multiplique $- 3.085$ por $0$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 18.96 \end{array}] + [\begin{array}{c} - 3.085 & 0 & 0 & 0 \\ 0 & - 3.085 & 0 & 0 \\ 0 & 0 & - 3.085 & 0 \\ - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 \end{array}]$

Etapa 4.13

Multiplique $- 3.085$ por $0$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 18.96 \end{array}] + [\begin{array}{c} - 3.085 & 0 & 0 & 0 \\ 0 & - 3.085 & 0 & 0 \\ 0 & 0 & - 3.085 & 0 \\ 0 & - 3.085 \cdot 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 \end{array}]$

Etapa 4.14

Multiplique $- 3.085$ por $0$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 18.96 \end{array}] + [\begin{array}{c} - 3.085 & 0 & 0 & 0 \\ 0 & - 3.085 & 0 & 0 \\ 0 & 0 & - 3.085 & 0 \\ 0 & 0 & - 3.085 \cdot 0 & - 3.085 \cdot 1 \end{array}]$

Etapa 4.15

Multiplique $- 3.085$ por $0$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 18.96 \end{array}] + [\begin{array}{c} - 3.085 & 0 & 0 & 0 \\ 0 & - 3.085 & 0 & 0 \\ 0 & 0 & - 3.085 & 0 \\ 0 & 0 & 0 & - 3.085 \cdot 1 \end{array}]$

Etapa 4.16

Multiplique $- 3.085$ por $1$ .

$[\begin{array}{c} 28 & 8.48 & - 13 & 20.8 \\ 16 & 12 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 18.96 \end{array}] + [\begin{array}{c} - 3.085 & 0 & 0 & 0 \\ 0 & - 3.085 & 0 & 0 \\ 0 & 0 & - 3.085 & 0 \\ 0 & 0 & 0 & - 3.085 \end{array}]$

Etapa 5

Adicione os elementos correspondentes.

$[\begin{array}{c} 28 - 3.085 & 8.48 + 0 & - 13 + 0 & 20.8 + 0 \\ 16 + 0 & 12 - 3.085 & 20 + 0 & - 8 + 0 \\ 4.92 + 0 & 20.84 + 0 & - 16.12 - 3.085 & 28.8 + 0 \\ 16.8 + 0 & 48.24 + 0 & - 12.34 + 0 & 18.96 - 3.085 \end{array}]$

Etapa 6

Simplify each element.

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Etapa 6.1

Subtraia $3.085$ de $28$ .

$[\begin{array}{c} 24.915 & 8.48 + 0 & - 13 + 0 & 20.8 + 0 \\ 16 + 0 & 12 - 3.085 & 20 + 0 & - 8 + 0 \\ 4.92 + 0 & 20.84 + 0 & - 16.12 - 3.085 & 28.8 + 0 \\ 16.8 + 0 & 48.24 + 0 & - 12.34 + 0 & 18.96 - 3.085 \end{array}]$

Etapa 6.2

Some $8.48$ e $0$ .

$[\begin{array}{c} 24.915 & 8.48 & - 13 + 0 & 20.8 + 0 \\ 16 + 0 & 12 - 3.085 & 20 + 0 & - 8 + 0 \\ 4.92 + 0 & 20.84 + 0 & - 16.12 - 3.085 & 28.8 + 0 \\ 16.8 + 0 & 48.24 + 0 & - 12.34 + 0 & 18.96 - 3.085 \end{array}]$

Etapa 6.3

Some $- 13$ e $0$ .

$[\begin{array}{c} 24.915 & 8.48 & - 13 & 20.8 + 0 \\ 16 + 0 & 12 - 3.085 & 20 + 0 & - 8 + 0 \\ 4.92 + 0 & 20.84 + 0 & - 16.12 - 3.085 & 28.8 + 0 \\ 16.8 + 0 & 48.24 + 0 & - 12.34 + 0 & 18.96 - 3.085 \end{array}]$

Etapa 6.4

Some $20.8$ e $0$ .

$[\begin{array}{c} 24.915 & 8.48 & - 13 & 20.8 \\ 16 + 0 & 12 - 3.085 & 20 + 0 & - 8 + 0 \\ 4.92 + 0 & 20.84 + 0 & - 16.12 - 3.085 & 28.8 + 0 \\ 16.8 + 0 & 48.24 + 0 & - 12.34 + 0 & 18.96 - 3.085 \end{array}]$

Etapa 6.5

Some $16$ e $0$ .

$[\begin{array}{c} 24.915 & 8.48 & - 13 & 20.8 \\ 16 & 12 - 3.085 & 20 + 0 & - 8 + 0 \\ 4.92 + 0 & 20.84 + 0 & - 16.12 - 3.085 & 28.8 + 0 \\ 16.8 + 0 & 48.24 + 0 & - 12.34 + 0 & 18.96 - 3.085 \end{array}]$

Etapa 6.6

Subtraia $3.085$ de $12$ .

$[\begin{array}{c} 24.915 & 8.48 & - 13 & 20.8 \\ 16 & 8.915 & 20 + 0 & - 8 + 0 \\ 4.92 + 0 & 20.84 + 0 & - 16.12 - 3.085 & 28.8 + 0 \\ 16.8 + 0 & 48.24 + 0 & - 12.34 + 0 & 18.96 - 3.085 \end{array}]$

Etapa 6.7

Some $20$ e $0$ .

$[\begin{array}{c} 24.915 & 8.48 & - 13 & 20.8 \\ 16 & 8.915 & 20 & - 8 + 0 \\ 4.92 + 0 & 20.84 + 0 & - 16.12 - 3.085 & 28.8 + 0 \\ 16.8 + 0 & 48.24 + 0 & - 12.34 + 0 & 18.96 - 3.085 \end{array}]$

Etapa 6.8

Some $- 8$ e $0$ .

$[\begin{array}{c} 24.915 & 8.48 & - 13 & 20.8 \\ 16 & 8.915 & 20 & - 8 \\ 4.92 + 0 & 20.84 + 0 & - 16.12 - 3.085 & 28.8 + 0 \\ 16.8 + 0 & 48.24 + 0 & - 12.34 + 0 & 18.96 - 3.085 \end{array}]$

Etapa 6.9

Some $4.92$ e $0$ .

$[\begin{array}{c} 24.915 & 8.48 & - 13 & 20.8 \\ 16 & 8.915 & 20 & - 8 \\ 4.92 & 20.84 + 0 & - 16.12 - 3.085 & 28.8 + 0 \\ 16.8 + 0 & 48.24 + 0 & - 12.34 + 0 & 18.96 - 3.085 \end{array}]$

Etapa 6.10

Some $20.84$ e $0$ .

$[\begin{array}{c} 24.915 & 8.48 & - 13 & 20.8 \\ 16 & 8.915 & 20 & - 8 \\ 4.92 & 20.84 & - 16.12 - 3.085 & 28.8 + 0 \\ 16.8 + 0 & 48.24 + 0 & - 12.34 + 0 & 18.96 - 3.085 \end{array}]$

Etapa 6.11

Subtraia $3.085$ de $- 16.12$ .

$[\begin{array}{c} 24.915 & 8.48 & - 13 & 20.8 \\ 16 & 8.915 & 20 & - 8 \\ 4.92 & 20.84 & - 19.205 & 28.8 + 0 \\ 16.8 + 0 & 48.24 + 0 & - 12.34 + 0 & 18.96 - 3.085 \end{array}]$

Etapa 6.12

Some $28.8$ e $0$ .

$[\begin{array}{c} 24.915 & 8.48 & - 13 & 20.8 \\ 16 & 8.915 & 20 & - 8 \\ 4.92 & 20.84 & - 19.205 & 28.8 \\ 16.8 + 0 & 48.24 + 0 & - 12.34 + 0 & 18.96 - 3.085 \end{array}]$

Etapa 6.13

Some $16.8$ e $0$ .

$[\begin{array}{c} 24.915 & 8.48 & - 13 & 20.8 \\ 16 & 8.915 & 20 & - 8 \\ 4.92 & 20.84 & - 19.205 & 28.8 \\ 16.8 & 48.24 + 0 & - 12.34 + 0 & 18.96 - 3.085 \end{array}]$

Etapa 6.14

Some $48.24$ e $0$ .

$[\begin{array}{c} 24.915 & 8.48 & - 13 & 20.8 \\ 16 & 8.915 & 20 & - 8 \\ 4.92 & 20.84 & - 19.205 & 28.8 \\ 16.8 & 48.24 & - 12.34 + 0 & 18.96 - 3.085 \end{array}]$

Etapa 6.15

Some $- 12.34$ e $0$ .

$[\begin{array}{c} 24.915 & 8.48 & - 13 & 20.8 \\ 16 & 8.915 & 20 & - 8 \\ 4.92 & 20.84 & - 19.205 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 18.96 - 3.085 \end{array}]$

Etapa 6.16

Subtraia $3.085$ de $18.96$ .

$[\begin{array}{c} 24.915 & 8.48 & - 13 & 20.8 \\ 16 & 8.915 & 20 & - 8 \\ 4.92 & 20.84 & - 19.205 & 28.8 \\ 16.8 & 48.24 & - 12.34 & 15.875 \end{array}]$

Etapa 7

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 7.1

Consider the corresponding sign chart.

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

Etapa 7.2

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

Etapa 7.3

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

$| \begin{array}{c} 8.915 & 20 & - 8 \\ 20.84 & - 19.205 & 28.8 \\ 48.24 & - 12.34 & 15.875 \end{array} |$

Etapa 7.4

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

$24.915 | \begin{array}{c} 8.915 & 20 & - 8 \\ 20.84 & - 19.205 & 28.8 \\ 48.24 & - 12.34 & 15.875 \end{array} |$

Etapa 7.5

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

$| \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} |$

Etapa 7.6

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

$- 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} |$

Etapa 7.7

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

$| \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} |$

Etapa 7.8

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

$- 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} |$

Etapa 7.9

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

$| \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 7.10

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

$- 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 7.11

Add the terms together.

$24.915 | \begin{array}{c} 8.915 & 20 & - 8 \\ 20.84 & - 19.205 & 28.8 \\ 48.24 & - 12.34 & 15.875 \end{array} | - 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} | - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 8

Avalie $| \begin{array}{c} 8.915 & 20 & - 8 \\ 20.84 & - 19.205 & 28.8 \\ 48.24 & - 12.34 & 15.875 \end{array} |$ .

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Etapa 8.1

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 8.1.1

Consider the corresponding sign chart.

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

Etapa 8.1.2

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

Etapa 8.1.3

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

$| \begin{array}{c} - 19.205 & 28.8 \\ - 12.34 & 15.875 \end{array} |$

Etapa 8.1.4

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

$8.915 | \begin{array}{c} - 19.205 & 28.8 \\ - 12.34 & 15.875 \end{array} |$

Etapa 8.1.5

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

$| \begin{array}{c} 20.84 & 28.8 \\ 48.24 & 15.875 \end{array} |$

Etapa 8.1.6

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

$- 20 | \begin{array}{c} 20.84 & 28.8 \\ 48.24 & 15.875 \end{array} |$

Etapa 8.1.7

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

$| \begin{array}{c} 20.84 & - 19.205 \\ 48.24 & - 12.34 \end{array} |$

Etapa 8.1.8

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

$- 8 | \begin{array}{c} 20.84 & - 19.205 \\ 48.24 & - 12.34 \end{array} |$

Etapa 8.1.9

Add the terms together.

$24.915 (8.915 | \begin{array}{c} - 19.205 & 28.8 \\ - 12.34 & 15.875 \end{array} | - 20 | \begin{array}{c} 20.84 & 28.8 \\ 48.24 & 15.875 \end{array} | - 8 | \begin{array}{c} 20.84 & - 19.205 \\ 48.24 & - 12.34 \end{array} |) - 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} | - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 8.2

Avalie $| \begin{array}{c} - 19.205 & 28.8 \\ - 12.34 & 15.875 \end{array} |$ .

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Etapa 8.2.1

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

$24.915 (8.915 (- 19.205 \cdot 15.875 - (- 12.34 \cdot 28.8)) - 20 | \begin{array}{c} 20.84 & 28.8 \\ 48.24 & 15.875 \end{array} | - 8 | \begin{array}{c} 20.84 & - 19.205 \\ 48.24 & - 12.34 \end{array} |) - 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} | - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 8.2.2

Simplifique o determinante.

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Etapa 8.2.2.1

Simplifique cada termo.

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Etapa 8.2.2.1.1

Multiplique $- 19.205$ por $15.875$ .

$24.915 (8.915 (- 304.879375 - (- 12.34 \cdot 28.8)) - 20 | \begin{array}{c} 20.84 & 28.8 \\ 48.24 & 15.875 \end{array} | - 8 | \begin{array}{c} 20.84 & - 19.205 \\ 48.24 & - 12.34 \end{array} |) - 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} | - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 8.2.2.1.2

Multiplique $- (- 12.34 \cdot 28.8)$ .

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Etapa 8.2.2.1.2.1

Multiplique $- 12.34$ por $28.8$ .

$24.915 (8.915 (- 304.879375 - - 355.392) - 20 | \begin{array}{c} 20.84 & 28.8 \\ 48.24 & 15.875 \end{array} | - 8 | \begin{array}{c} 20.84 & - 19.205 \\ 48.24 & - 12.34 \end{array} |) - 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} | - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 8.2.2.1.2.2

Multiplique $- 1$ por $- 355.392$ .

$24.915 (8.915 (- 304.879375 + 355.392) - 20 | \begin{array}{c} 20.84 & 28.8 \\ 48.24 & 15.875 \end{array} | - 8 | \begin{array}{c} 20.84 & - 19.205 \\ 48.24 & - 12.34 \end{array} |) - 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} | - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 8.2.2.2

Some $- 304.879375$ e $355.392$ .

$24.915 (8.915 \cdot 50.512625 - 20 | \begin{array}{c} 20.84 & 28.8 \\ 48.24 & 15.875 \end{array} | - 8 | \begin{array}{c} 20.84 & - 19.205 \\ 48.24 & - 12.34 \end{array} |) - 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} | - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 8.3

Avalie $| \begin{array}{c} 20.84 & 28.8 \\ 48.24 & 15.875 \end{array} |$ .

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Etapa 8.3.1

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

$24.915 (8.915 \cdot 50.512625 - 20 (20.84 \cdot 15.875 - 48.24 \cdot 28.8) - 8 | \begin{array}{c} 20.84 & - 19.205 \\ 48.24 & - 12.34 \end{array} |) - 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} | - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 8.3.2

Simplifique o determinante.

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Etapa 8.3.2.1

Simplifique cada termo.

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Etapa 8.3.2.1.1

Multiplique $20.84$ por $15.875$ .

$24.915 (8.915 \cdot 50.512625 - 20 (330.835 - 48.24 \cdot 28.8) - 8 | \begin{array}{c} 20.84 & - 19.205 \\ 48.24 & - 12.34 \end{array} |) - 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} | - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 8.3.2.1.2

Multiplique $- 48.24$ por $28.8$ .

$24.915 (8.915 \cdot 50.512625 - 20 (330.835 - 1389.312) - 8 | \begin{array}{c} 20.84 & - 19.205 \\ 48.24 & - 12.34 \end{array} |) - 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} | - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 8.3.2.2

Subtraia $1389.312$ de $330.835$ .

$24.915 (8.915 \cdot 50.512625 - 20 \cdot - 1058.477 - 8 | \begin{array}{c} 20.84 & - 19.205 \\ 48.24 & - 12.34 \end{array} |) - 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} | - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 8.4

Avalie $| \begin{array}{c} 20.84 & - 19.205 \\ 48.24 & - 12.34 \end{array} |$ .

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Etapa 8.4.1

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

$24.915 (8.915 \cdot 50.512625 - 20 \cdot - 1058.477 - 8 (20.84 \cdot - 12.34 - 48.24 \cdot - 19.205)) - 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} | - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 8.4.2

Simplifique o determinante.

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Etapa 8.4.2.1

Simplifique cada termo.

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Etapa 8.4.2.1.1

Multiplique $20.84$ por $- 12.34$ .

$24.915 (8.915 \cdot 50.512625 - 20 \cdot - 1058.477 - 8 (- 257.1656 - 48.24 \cdot - 19.205)) - 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} | - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 8.4.2.1.2

Multiplique $- 48.24$ por $- 19.205$ .

$24.915 (8.915 \cdot 50.512625 - 20 \cdot - 1058.477 - 8 (- 257.1656 + 926.4492)) - 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} | - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 8.4.2.2

Some $- 257.1656$ e $926.4492$ .

$24.915 (8.915 \cdot 50.512625 - 20 \cdot - 1058.477 - 8 \cdot 669.2836) - 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} | - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 8.5

Simplifique o determinante.

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Etapa 8.5.1

Simplifique cada termo.

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Etapa 8.5.1.1

Multiplique $8.915$ por $50.512625$ .

$24.915 (450.32005187 - 20 \cdot - 1058.477 - 8 \cdot 669.2836) - 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} | - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 8.5.1.2

Multiplique $- 20$ por $- 1058.477$ .

$24.915 (450.32005187 + 21169.54 - 8 \cdot 669.2836) - 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} | - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 8.5.1.3

Multiplique $- 8$ por $669.2836$ .

$24.915 (450.32005187 + 21169.54 - 5354.2688) - 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} | - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 8.5.2

Some $450.32005187$ e $21169.54$ .

$24.915 (21619.86005187 - 5354.2688) - 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} | - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 8.5.3

Subtraia $5354.2688$ de $21619.86005187$ .

$24.915 \cdot 16265.59125187 - 8.48 | \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} | - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 9

Avalie $| \begin{array}{c} 16 & 20 & - 8 \\ 4.92 & - 19.205 & 28.8 \\ 16.8 & - 12.34 & 15.875 \end{array} |$ .

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Etapa 9.1

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 9.1.1

Consider the corresponding sign chart.

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

Etapa 9.1.2

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

Etapa 9.1.3

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

$| \begin{array}{c} - 19.205 & 28.8 \\ - 12.34 & 15.875 \end{array} |$

Etapa 9.1.4

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

$16 | \begin{array}{c} - 19.205 & 28.8 \\ - 12.34 & 15.875 \end{array} |$

Etapa 9.1.5

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

$| \begin{array}{c} 4.92 & 28.8 \\ 16.8 & 15.875 \end{array} |$

Etapa 9.1.6

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

$- 20 | \begin{array}{c} 4.92 & 28.8 \\ 16.8 & 15.875 \end{array} |$

Etapa 9.1.7

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

$| \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} |$

Etapa 9.1.8

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

$- 8 | \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} |$

Etapa 9.1.9

Add the terms together.

$24.915 \cdot 16265.59125187 - 8.48 (16 | \begin{array}{c} - 19.205 & 28.8 \\ - 12.34 & 15.875 \end{array} | - 20 | \begin{array}{c} 4.92 & 28.8 \\ 16.8 & 15.875 \end{array} | - 8 | \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} |) - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 9.2

Avalie $| \begin{array}{c} - 19.205 & 28.8 \\ - 12.34 & 15.875 \end{array} |$ .

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Etapa 9.2.1

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

$24.915 \cdot 16265.59125187 - 8.48 (16 (- 19.205 \cdot 15.875 - (- 12.34 \cdot 28.8)) - 20 | \begin{array}{c} 4.92 & 28.8 \\ 16.8 & 15.875 \end{array} | - 8 | \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} |) - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 9.2.2

Simplifique o determinante.

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Etapa 9.2.2.1

Simplifique cada termo.

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Etapa 9.2.2.1.1

Multiplique $- 19.205$ por $15.875$ .

$24.915 \cdot 16265.59125187 - 8.48 (16 (- 304.879375 - (- 12.34 \cdot 28.8)) - 20 | \begin{array}{c} 4.92 & 28.8 \\ 16.8 & 15.875 \end{array} | - 8 | \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} |) - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 9.2.2.1.2

Multiplique $- (- 12.34 \cdot 28.8)$ .

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Etapa 9.2.2.1.2.1

Multiplique $- 12.34$ por $28.8$ .

$24.915 \cdot 16265.59125187 - 8.48 (16 (- 304.879375 - - 355.392) - 20 | \begin{array}{c} 4.92 & 28.8 \\ 16.8 & 15.875 \end{array} | - 8 | \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} |) - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 9.2.2.1.2.2

Multiplique $- 1$ por $- 355.392$ .

$24.915 \cdot 16265.59125187 - 8.48 (16 (- 304.879375 + 355.392) - 20 | \begin{array}{c} 4.92 & 28.8 \\ 16.8 & 15.875 \end{array} | - 8 | \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} |) - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 9.2.2.2

Some $- 304.879375$ e $355.392$ .

$24.915 \cdot 16265.59125187 - 8.48 (16 \cdot 50.512625 - 20 | \begin{array}{c} 4.92 & 28.8 \\ 16.8 & 15.875 \end{array} | - 8 | \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} |) - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 9.3

Avalie $| \begin{array}{c} 4.92 & 28.8 \\ 16.8 & 15.875 \end{array} |$ .

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Etapa 9.3.1

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

$24.915 \cdot 16265.59125187 - 8.48 (16 \cdot 50.512625 - 20 (4.92 \cdot 15.875 - 16.8 \cdot 28.8) - 8 | \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} |) - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 9.3.2

Simplifique o determinante.

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Etapa 9.3.2.1

Simplifique cada termo.

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Etapa 9.3.2.1.1

Multiplique $4.92$ por $15.875$ .

$24.915 \cdot 16265.59125187 - 8.48 (16 \cdot 50.512625 - 20 (78.105 - 16.8 \cdot 28.8) - 8 | \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} |) - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 9.3.2.1.2

Multiplique $- 16.8$ por $28.8$ .

$24.915 \cdot 16265.59125187 - 8.48 (16 \cdot 50.512625 - 20 (78.105 - 483.84) - 8 | \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} |) - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 9.3.2.2

Subtraia $483.84$ de $78.105$ .

$24.915 \cdot 16265.59125187 - 8.48 (16 \cdot 50.512625 - 20 \cdot - 405.735 - 8 | \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} |) - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 9.4

Avalie $| \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} |$ .

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Etapa 9.4.1

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

$24.915 \cdot 16265.59125187 - 8.48 (16 \cdot 50.512625 - 20 \cdot - 405.735 - 8 (4.92 \cdot - 12.34 - 16.8 \cdot - 19.205)) - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 9.4.2

Simplifique o determinante.

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Etapa 9.4.2.1

Simplifique cada termo.

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Etapa 9.4.2.1.1

Multiplique $4.92$ por $- 12.34$ .

$24.915 \cdot 16265.59125187 - 8.48 (16 \cdot 50.512625 - 20 \cdot - 405.735 - 8 (- 60.7128 - 16.8 \cdot - 19.205)) - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 9.4.2.1.2

Multiplique $- 16.8$ por $- 19.205$ .

$24.915 \cdot 16265.59125187 - 8.48 (16 \cdot 50.512625 - 20 \cdot - 405.735 - 8 (- 60.7128 + 322.644)) - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 9.4.2.2

Some $- 60.7128$ e $322.644$ .

$24.915 \cdot 16265.59125187 - 8.48 (16 \cdot 50.512625 - 20 \cdot - 405.735 - 8 \cdot 261.9312) - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 9.5

Simplifique o determinante.

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Etapa 9.5.1

Simplifique cada termo.

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Etapa 9.5.1.1

Multiplique $16$ por $50.512625$ .

$24.915 \cdot 16265.59125187 - 8.48 (808.202 - 20 \cdot - 405.735 - 8 \cdot 261.9312) - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 9.5.1.2

Multiplique $- 20$ por $- 405.735$ .

$24.915 \cdot 16265.59125187 - 8.48 (808.202 + 8114.7 - 8 \cdot 261.9312) - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 9.5.1.3

Multiplique $- 8$ por $261.9312$ .

$24.915 \cdot 16265.59125187 - 8.48 (808.202 + 8114.7 - 2095.4496) - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 9.5.2

Some $808.202$ e $8114.7$ .

$24.915 \cdot 16265.59125187 - 8.48 (8922.902 - 2095.4496) - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 9.5.3

Subtraia $2095.4496$ de $8922.902$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 | \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} | - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 10

Avalie $| \begin{array}{c} 16 & 8.915 & - 8 \\ 4.92 & 20.84 & 28.8 \\ 16.8 & 48.24 & 15.875 \end{array} |$ .

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Etapa 10.1

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 10.1.1

Consider the corresponding sign chart.

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

Etapa 10.1.2

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

Etapa 10.1.3

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

$| \begin{array}{c} 20.84 & 28.8 \\ 48.24 & 15.875 \end{array} |$

Etapa 10.1.4

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

$16 | \begin{array}{c} 20.84 & 28.8 \\ 48.24 & 15.875 \end{array} |$

Etapa 10.1.5

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

$| \begin{array}{c} 4.92 & 28.8 \\ 16.8 & 15.875 \end{array} |$

Etapa 10.1.6

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

$- 8.915 | \begin{array}{c} 4.92 & 28.8 \\ 16.8 & 15.875 \end{array} |$

Etapa 10.1.7

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

$| \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |$

Etapa 10.1.8

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

$- 8 | \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |$

Etapa 10.1.9

Add the terms together.

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 (16 | \begin{array}{c} 20.84 & 28.8 \\ 48.24 & 15.875 \end{array} | - 8.915 | \begin{array}{c} 4.92 & 28.8 \\ 16.8 & 15.875 \end{array} | - 8 | \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |) - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 10.2

Avalie $| \begin{array}{c} 20.84 & 28.8 \\ 48.24 & 15.875 \end{array} |$ .

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Etapa 10.2.1

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

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 (16 (20.84 \cdot 15.875 - 48.24 \cdot 28.8) - 8.915 | \begin{array}{c} 4.92 & 28.8 \\ 16.8 & 15.875 \end{array} | - 8 | \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |) - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 10.2.2

Simplifique o determinante.

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Etapa 10.2.2.1

Simplifique cada termo.

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Etapa 10.2.2.1.1

Multiplique $20.84$ por $15.875$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 (16 (330.835 - 48.24 \cdot 28.8) - 8.915 | \begin{array}{c} 4.92 & 28.8 \\ 16.8 & 15.875 \end{array} | - 8 | \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |) - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 10.2.2.1.2

Multiplique $- 48.24$ por $28.8$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 (16 (330.835 - 1389.312) - 8.915 | \begin{array}{c} 4.92 & 28.8 \\ 16.8 & 15.875 \end{array} | - 8 | \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |) - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 10.2.2.2

Subtraia $1389.312$ de $330.835$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 (16 \cdot - 1058.477 - 8.915 | \begin{array}{c} 4.92 & 28.8 \\ 16.8 & 15.875 \end{array} | - 8 | \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |) - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 10.3

Avalie $| \begin{array}{c} 4.92 & 28.8 \\ 16.8 & 15.875 \end{array} |$ .

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Etapa 10.3.1

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

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 (16 \cdot - 1058.477 - 8.915 (4.92 \cdot 15.875 - 16.8 \cdot 28.8) - 8 | \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |) - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 10.3.2

Simplifique o determinante.

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Etapa 10.3.2.1

Simplifique cada termo.

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Etapa 10.3.2.1.1

Multiplique $4.92$ por $15.875$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 (16 \cdot - 1058.477 - 8.915 (78.105 - 16.8 \cdot 28.8) - 8 | \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |) - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 10.3.2.1.2

Multiplique $- 16.8$ por $28.8$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 (16 \cdot - 1058.477 - 8.915 (78.105 - 483.84) - 8 | \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |) - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 10.3.2.2

Subtraia $483.84$ de $78.105$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 (16 \cdot - 1058.477 - 8.915 \cdot - 405.735 - 8 | \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |) - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 10.4

Avalie $| \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |$ .

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Etapa 10.4.1

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

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 (16 \cdot - 1058.477 - 8.915 \cdot - 405.735 - 8 (4.92 \cdot 48.24 - 16.8 \cdot 20.84)) - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 10.4.2

Simplifique o determinante.

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Etapa 10.4.2.1

Simplifique cada termo.

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Etapa 10.4.2.1.1

Multiplique $4.92$ por $48.24$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 (16 \cdot - 1058.477 - 8.915 \cdot - 405.735 - 8 (237.3408 - 16.8 \cdot 20.84)) - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 10.4.2.1.2

Multiplique $- 16.8$ por $20.84$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 (16 \cdot - 1058.477 - 8.915 \cdot - 405.735 - 8 (237.3408 - 350.112)) - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 10.4.2.2

Subtraia $350.112$ de $237.3408$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 (16 \cdot - 1058.477 - 8.915 \cdot - 405.735 - 8 \cdot - 112.7712) - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 10.5

Simplifique o determinante.

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Etapa 10.5.1

Simplifique cada termo.

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Etapa 10.5.1.1

Multiplique $16$ por $- 1058.477$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 (- 16935.632 - 8.915 \cdot - 405.735 - 8 \cdot - 112.7712) - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 10.5.1.2

Multiplique $- 8.915$ por $- 405.735$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 (- 16935.632 + 3617.127525 - 8 \cdot - 112.7712) - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 10.5.1.3

Multiplique $- 8$ por $- 112.7712$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 (- 16935.632 + 3617.127525 + 902.1696) - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 10.5.2

Some $- 16935.632$ e $3617.127525$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 (- 13318.504475 + 902.1696) - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 10.5.3

Some $- 13318.504475$ e $902.1696$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 \cdot - 12416.334875 - 20.8 | \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$

Etapa 11

Avalie $| \begin{array}{c} 16 & 8.915 & 20 \\ 4.92 & 20.84 & - 19.205 \\ 16.8 & 48.24 & - 12.34 \end{array} |$ .

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Etapa 11.1

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 11.1.1

Consider the corresponding sign chart.

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

Etapa 11.1.2

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

Etapa 11.1.3

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

$| \begin{array}{c} 20.84 & - 19.205 \\ 48.24 & - 12.34 \end{array} |$

Etapa 11.1.4

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

$16 | \begin{array}{c} 20.84 & - 19.205 \\ 48.24 & - 12.34 \end{array} |$

Etapa 11.1.5

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

$| \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} |$

Etapa 11.1.6

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

$- 8.915 | \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} |$

Etapa 11.1.7

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

$| \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |$

Etapa 11.1.8

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

$20 | \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |$

Etapa 11.1.9

Add the terms together.

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 \cdot - 12416.334875 - 20.8 (16 | \begin{array}{c} 20.84 & - 19.205 \\ 48.24 & - 12.34 \end{array} | - 8.915 | \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} | + 20 | \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |)$

Etapa 11.2

Avalie $| \begin{array}{c} 20.84 & - 19.205 \\ 48.24 & - 12.34 \end{array} |$ .

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Etapa 11.2.1

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

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 \cdot - 12416.334875 - 20.8 (16 (20.84 \cdot - 12.34 - 48.24 \cdot - 19.205) - 8.915 | \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} | + 20 | \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |)$

Etapa 11.2.2

Simplifique o determinante.

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Etapa 11.2.2.1

Simplifique cada termo.

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Etapa 11.2.2.1.1

Multiplique $20.84$ por $- 12.34$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 \cdot - 12416.334875 - 20.8 (16 (- 257.1656 - 48.24 \cdot - 19.205) - 8.915 | \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} | + 20 | \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |)$

Etapa 11.2.2.1.2

Multiplique $- 48.24$ por $- 19.205$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 \cdot - 12416.334875 - 20.8 (16 (- 257.1656 + 926.4492) - 8.915 | \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} | + 20 | \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |)$

Etapa 11.2.2.2

Some $- 257.1656$ e $926.4492$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 \cdot - 12416.334875 - 20.8 (16 \cdot 669.2836 - 8.915 | \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} | + 20 | \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |)$

Etapa 11.3

Avalie $| \begin{array}{c} 4.92 & - 19.205 \\ 16.8 & - 12.34 \end{array} |$ .

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Etapa 11.3.1

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

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 \cdot - 12416.334875 - 20.8 (16 \cdot 669.2836 - 8.915 (4.92 \cdot - 12.34 - 16.8 \cdot - 19.205) + 20 | \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |)$

Etapa 11.3.2

Simplifique o determinante.

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Etapa 11.3.2.1

Simplifique cada termo.

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Etapa 11.3.2.1.1

Multiplique $4.92$ por $- 12.34$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 \cdot - 12416.334875 - 20.8 (16 \cdot 669.2836 - 8.915 (- 60.7128 - 16.8 \cdot - 19.205) + 20 | \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |)$

Etapa 11.3.2.1.2

Multiplique $- 16.8$ por $- 19.205$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 \cdot - 12416.334875 - 20.8 (16 \cdot 669.2836 - 8.915 (- 60.7128 + 322.644) + 20 | \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |)$

Etapa 11.3.2.2

Some $- 60.7128$ e $322.644$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 \cdot - 12416.334875 - 20.8 (16 \cdot 669.2836 - 8.915 \cdot 261.9312 + 20 | \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |)$

Etapa 11.4

Avalie $| \begin{array}{c} 4.92 & 20.84 \\ 16.8 & 48.24 \end{array} |$ .

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Etapa 11.4.1

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

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 \cdot - 12416.334875 - 20.8 (16 \cdot 669.2836 - 8.915 \cdot 261.9312 + 20 (4.92 \cdot 48.24 - 16.8 \cdot 20.84))$

Etapa 11.4.2

Simplifique o determinante.

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Etapa 11.4.2.1

Simplifique cada termo.

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Etapa 11.4.2.1.1

Multiplique $4.92$ por $48.24$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 \cdot - 12416.334875 - 20.8 (16 \cdot 669.2836 - 8.915 \cdot 261.9312 + 20 (237.3408 - 16.8 \cdot 20.84))$

Etapa 11.4.2.1.2

Multiplique $- 16.8$ por $20.84$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 \cdot - 12416.334875 - 20.8 (16 \cdot 669.2836 - 8.915 \cdot 261.9312 + 20 (237.3408 - 350.112))$

Etapa 11.4.2.2

Subtraia $350.112$ de $237.3408$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 \cdot - 12416.334875 - 20.8 (16 \cdot 669.2836 - 8.915 \cdot 261.9312 + 20 \cdot - 112.7712)$

Etapa 11.5

Simplifique o determinante.

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Etapa 11.5.1

Simplifique cada termo.

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Etapa 11.5.1.1

Multiplique $16$ por $669.2836$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 \cdot - 12416.334875 - 20.8 (10708.5376 - 8.915 \cdot 261.9312 + 20 \cdot - 112.7712)$

Etapa 11.5.1.2

Multiplique $- 8.915$ por $261.9312$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 \cdot - 12416.334875 - 20.8 (10708.5376 - 2335.116648 + 20 \cdot - 112.7712)$

Etapa 11.5.1.3

Multiplique $20$ por $- 112.7712$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 \cdot - 12416.334875 - 20.8 (10708.5376 - 2335.116648 - 2255.424)$

Etapa 11.5.2

Subtraia $2335.116648$ de $10708.5376$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 \cdot - 12416.334875 - 20.8 (8373.420952 - 2255.424)$

Etapa 11.5.3

Subtraia $2255.424$ de $8373.420952$ .

$24.915 \cdot 16265.59125187 - 8.48 \cdot 6827.4524 - 13 \cdot - 12416.334875 - 20.8 \cdot 6117.996952$

Etapa 12

Simplifique o determinante.

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Etapa 12.1

Simplifique cada termo.

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Etapa 12.1.1

Multiplique $24.915$ por $16265.59125187$ .

$405257.20604046 - 8.48 \cdot 6827.4524 - 13 \cdot - 12416.334875 - 20.8 \cdot 6117.996952$

Etapa 12.1.2

Multiplique $- 8.48$ por $6827.4524$ .

$405257.20604046 - 57896.796352 - 13 \cdot - 12416.334875 - 20.8 \cdot 6117.996952$

Etapa 12.1.3

Multiplique $- 13$ por $- 12416.334875$ .

$405257.20604046 - 57896.796352 + 161412.353375 - 20.8 \cdot 6117.996952$

Etapa 12.1.4

Multiplique $- 20.8$ por $6117.996952$ .

$405257.20604046 - 57896.796352 + 161412.353375 - 127254.3366016$

Etapa 12.2

Subtraia $57896.796352$ de $405257.20604046$ .

$347360.40968846 + 161412.353375 - 127254.3366016$

Etapa 12.3

Some $347360.40968846$ e $161412.353375$ .

$508772.76306346 - 127254.3366016$

Etapa 12.4

Subtraia $127254.3366016$ de $508772.76306346$ .

$381518.42646186$