Álgebra lineal Ejemplos

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

Paso 1

Simplifica cada término.

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Paso 1.1

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

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

Paso 1.2

Multiplica $4$ por cada elemento de la matriz.

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

Paso 1.3

Simplifica cada elemento de la matriz.

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Paso 1.3.1

Multiplica $4$ por $7$ .

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

Paso 1.3.2

Multiplica $4$ por $2.12$ .

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

Paso 1.3.3

Multiplica $4$ por $- 3.25$ .

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

Paso 1.3.4

Multiplica $4$ por $5.2$ .

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

Paso 1.3.5

Multiplica $4$ por $4$ .

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

Paso 1.3.6

Multiplica $4$ por $3$ .

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

Paso 1.3.7

Multiplica $4$ por $5$ .

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

Paso 1.3.8

Multiplica $4$ por $- 2$ .

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

Paso 1.3.9

Multiplica $4$ por $1.23$ .

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

Paso 1.3.10

Multiplica $4$ por $5.21$ .

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

Paso 1.3.11

Multiplica $4$ por $- 4.03$ .

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

Paso 1.3.12

Multiplica $4$ por $7.2$ .

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

Paso 1.3.13

Multiplica $4$ por $4.2$ .

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

Paso 1.3.14

Multiplica $4$ por $12.06$ .

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

Paso 1.3.15

Multiplica $4$ por $- 3.085$ .

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

Paso 1.3.16

Multiplica $4$ por $4.74$ .

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

Paso 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.

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

Paso 3

Multiplica $- 3.085$ por cada elemento de la matriz.

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

Paso 4

Simplifica cada elemento de la matriz.

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Paso 4.1

Multiplica $- 3.085$ por $1$ .

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

Paso 4.2

Multiplica $- 3.085$ por $0$ .

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

Paso 4.3

Multiplica $- 3.085$ por $0$ .

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

Paso 4.4

Multiplica $- 3.085$ por $0$ .

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

Paso 4.5

Multiplica $- 3.085$ por $0$ .

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

Paso 4.6

Multiplica $- 3.085$ por $1$ .

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

Paso 4.7

Multiplica $- 3.085$ por $0$ .

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

Paso 4.8

Multiplica $- 3.085$ por $0$ .

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

Paso 4.9

Multiplica $- 3.085$ por $0$ .

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

Paso 4.10

Multiplica $- 3.085$ por $0$ .

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

Paso 4.11

Multiplica $- 3.085$ por $1$ .

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

Paso 4.12

Multiplica $- 3.085$ por $0$ .

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

Paso 4.13

Multiplica $- 3.085$ por $0$ .

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

Paso 4.14

Multiplica $- 3.085$ por $0$ .

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

Paso 4.15

Multiplica $- 3.085$ por $0$ .

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

Paso 4.16

Multiplica $- 3.085$ por $1$ .

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

Paso 5

Suma los elementos correspondientes.

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

Paso 6

Simplify each element.

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Paso 6.1

Resta $3.085$ de $28$ .

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

Paso 6.2

Suma $8.48$ y $0$ .

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

Paso 6.3

Suma $- 13$ y $0$ .

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

Paso 6.4

Suma $20.8$ y $0$ .

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

Paso 6.5

Suma $16$ y $0$ .

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

Paso 6.6

Resta $3.085$ de $12$ .

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

Paso 6.7

Suma $20$ y $0$ .

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

Paso 6.8

Suma $- 8$ y $0$ .

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

Paso 6.9

Suma $4.92$ y $0$ .

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

Paso 6.10

Suma $20.84$ y $0$ .

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

Paso 6.11

Resta $3.085$ de $- 16.12$ .

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

Paso 6.12

Suma $28.8$ y $0$ .

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

Paso 6.13

Suma $16.8$ y $0$ .

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

Paso 6.14

Suma $48.24$ y $0$ .

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

Paso 6.15

Suma $- 12.34$ y $0$ .

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

Paso 6.16

Resta $3.085$ de $18.96$ .

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

Paso 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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Paso 7.1

Consider the corresponding sign chart.

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

Paso 7.2

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

Paso 7.3

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

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

Paso 7.4

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

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

Paso 7.5

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

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

Paso 7.6

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

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

Paso 7.7

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

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

Paso 7.8

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

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

Paso 7.9

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

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

Paso 7.10

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

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

Paso 7.11

Add the terms together.

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

Paso 8

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

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Paso 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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Paso 8.1.1

Consider the corresponding sign chart.

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

Paso 8.1.2

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

Paso 8.1.3

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

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

Paso 8.1.4

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

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

Paso 8.1.5

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

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

Paso 8.1.6

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

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

Paso 8.1.7

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

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

Paso 8.1.8

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

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

Paso 8.1.9

Add the terms together.

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

Paso 8.2

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

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Paso 8.2.1

El determinante de una matriz $2 \times 2$ puede obtenerse usando la fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Paso 8.2.2

Simplifica el determinante.

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Paso 8.2.2.1

Simplifica cada término.

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Paso 8.2.2.1.1

Multiplica $- 19.205$ por $15.875$ .

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

Paso 8.2.2.1.2

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

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Paso 8.2.2.1.2.1

Multiplica $- 12.34$ por $28.8$ .

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

Paso 8.2.2.1.2.2

Multiplica $- 1$ por $- 355.392$ .

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

Paso 8.2.2.2

Suma $- 304.879375$ y $355.392$ .

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

Paso 8.3

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

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Paso 8.3.1

El determinante de una matriz $2 \times 2$ puede obtenerse usando la fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Paso 8.3.2

Simplifica el determinante.

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Paso 8.3.2.1

Simplifica cada término.

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Paso 8.3.2.1.1

Multiplica $20.84$ por $15.875$ .

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

Paso 8.3.2.1.2

Multiplica $- 48.24$ por $28.8$ .

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

Paso 8.3.2.2

Resta $1389.312$ de $330.835$ .

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

Paso 8.4

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

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Paso 8.4.1

El determinante de una matriz $2 \times 2$ puede obtenerse usando la fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Paso 8.4.2

Simplifica el determinante.

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Paso 8.4.2.1

Simplifica cada término.

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Paso 8.4.2.1.1

Multiplica $20.84$ por $- 12.34$ .

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

Paso 8.4.2.1.2

Multiplica $- 48.24$ por $- 19.205$ .

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

Paso 8.4.2.2

Suma $- 257.1656$ y $926.4492$ .

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

Paso 8.5

Simplifica el determinante.

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Paso 8.5.1

Simplifica cada término.

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Paso 8.5.1.1

Multiplica $8.915$ por $50.512625$ .

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

Paso 8.5.1.2

Multiplica $- 20$ por $- 1058.477$ .

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

Paso 8.5.1.3

Multiplica $- 8$ por $669.2836$ .

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

Paso 8.5.2

Suma $450.32005187$ y $21169.54$ .

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

Paso 8.5.3

Resta $5354.2688$ de $21619.86005187$ .

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

Paso 9

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

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Paso 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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Paso 9.1.1

Consider the corresponding sign chart.

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

Paso 9.1.2

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

Paso 9.1.3

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

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

Paso 9.1.4

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

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

Paso 9.1.5

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

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

Paso 9.1.6

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

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

Paso 9.1.7

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

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

Paso 9.1.8

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

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

Paso 9.1.9

Add the terms together.

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

Paso 9.2

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

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Paso 9.2.1

El determinante de una matriz $2 \times 2$ puede obtenerse usando la fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Paso 9.2.2

Simplifica el determinante.

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Paso 9.2.2.1

Simplifica cada término.

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Paso 9.2.2.1.1

Multiplica $- 19.205$ por $15.875$ .

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

Paso 9.2.2.1.2

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

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Paso 9.2.2.1.2.1

Multiplica $- 12.34$ por $28.8$ .

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

Paso 9.2.2.1.2.2

Multiplica $- 1$ por $- 355.392$ .

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

Paso 9.2.2.2

Suma $- 304.879375$ y $355.392$ .

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

Paso 9.3

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

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Paso 9.3.1

El determinante de una matriz $2 \times 2$ puede obtenerse usando la fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Paso 9.3.2

Simplifica el determinante.

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Paso 9.3.2.1

Simplifica cada término.

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Paso 9.3.2.1.1

Multiplica $4.92$ por $15.875$ .

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

Paso 9.3.2.1.2

Multiplica $- 16.8$ por $28.8$ .

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

Paso 9.3.2.2

Resta $483.84$ de $78.105$ .

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

Paso 9.4

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

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Paso 9.4.1

El determinante de una matriz $2 \times 2$ puede obtenerse usando la fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Paso 9.4.2

Simplifica el determinante.

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Paso 9.4.2.1

Simplifica cada término.

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Paso 9.4.2.1.1

Multiplica $4.92$ por $- 12.34$ .

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

Paso 9.4.2.1.2

Multiplica $- 16.8$ por $- 19.205$ .

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

Paso 9.4.2.2

Suma $- 60.7128$ y $322.644$ .

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

Paso 9.5

Simplifica el determinante.

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Paso 9.5.1

Simplifica cada término.

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Paso 9.5.1.1

Multiplica $16$ por $50.512625$ .

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

Paso 9.5.1.2

Multiplica $- 20$ por $- 405.735$ .

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

Paso 9.5.1.3

Multiplica $- 8$ por $261.9312$ .

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

Paso 9.5.2

Suma $808.202$ y $8114.7$ .

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

Paso 9.5.3

Resta $2095.4496$ de $8922.902$ .

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

Paso 10

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

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Paso 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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Paso 10.1.1

Consider the corresponding sign chart.

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

Paso 10.1.2

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

Paso 10.1.3

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

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

Paso 10.1.4

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

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

Paso 10.1.5

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

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

Paso 10.1.6

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

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

Paso 10.1.7

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

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

Paso 10.1.8

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

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

Paso 10.1.9

Add the terms together.

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

Paso 10.2

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

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Paso 10.2.1

El determinante de una matriz $2 \times 2$ puede obtenerse usando la fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Paso 10.2.2

Simplifica el determinante.

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Paso 10.2.2.1

Simplifica cada término.

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Paso 10.2.2.1.1

Multiplica $20.84$ por $15.875$ .

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

Paso 10.2.2.1.2

Multiplica $- 48.24$ por $28.8$ .

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

Paso 10.2.2.2

Resta $1389.312$ de $330.835$ .

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

Paso 10.3

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

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Paso 10.3.1

El determinante de una matriz $2 \times 2$ puede obtenerse usando la fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Paso 10.3.2

Simplifica el determinante.

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Paso 10.3.2.1

Simplifica cada término.

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Paso 10.3.2.1.1

Multiplica $4.92$ por $15.875$ .

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

Paso 10.3.2.1.2

Multiplica $- 16.8$ por $28.8$ .

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

Paso 10.3.2.2

Resta $483.84$ de $78.105$ .

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

Paso 10.4

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

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Paso 10.4.1

El determinante de una matriz $2 \times 2$ puede obtenerse usando la fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Paso 10.4.2

Simplifica el determinante.

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Paso 10.4.2.1

Simplifica cada término.

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Paso 10.4.2.1.1

Multiplica $4.92$ por $48.24$ .

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

Paso 10.4.2.1.2

Multiplica $- 16.8$ por $20.84$ .

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

Paso 10.4.2.2

Resta $350.112$ de $237.3408$ .

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

Paso 10.5

Simplifica el determinante.

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Paso 10.5.1

Simplifica cada término.

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Paso 10.5.1.1

Multiplica $16$ por $- 1058.477$ .

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

Paso 10.5.1.2

Multiplica $- 8.915$ por $- 405.735$ .

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

Paso 10.5.1.3

Multiplica $- 8$ por $- 112.7712$ .

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

Paso 10.5.2

Suma $- 16935.632$ y $3617.127525$ .

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

Paso 10.5.3

Suma $- 13318.504475$ y $902.1696$ .

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

Paso 11

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

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Paso 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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Paso 11.1.1

Consider the corresponding sign chart.

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

Paso 11.1.2

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

Paso 11.1.3

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

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

Paso 11.1.4

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

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

Paso 11.1.5

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

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

Paso 11.1.6

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

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

Paso 11.1.7

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

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

Paso 11.1.8

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

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

Paso 11.1.9

Add the terms together.

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

Paso 11.2

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

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Paso 11.2.1

El determinante de una matriz $2 \times 2$ puede obtenerse usando la fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Paso 11.2.2

Simplifica el determinante.

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Paso 11.2.2.1

Simplifica cada término.

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Paso 11.2.2.1.1

Multiplica $20.84$ por $- 12.34$ .

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

Paso 11.2.2.1.2

Multiplica $- 48.24$ por $- 19.205$ .

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

Paso 11.2.2.2

Suma $- 257.1656$ y $926.4492$ .

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

Paso 11.3

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

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Paso 11.3.1

El determinante de una matriz $2 \times 2$ puede obtenerse usando la fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Paso 11.3.2

Simplifica el determinante.

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Paso 11.3.2.1

Simplifica cada término.

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Paso 11.3.2.1.1

Multiplica $4.92$ por $- 12.34$ .

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

Paso 11.3.2.1.2

Multiplica $- 16.8$ por $- 19.205$ .

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

Paso 11.3.2.2

Suma $- 60.7128$ y $322.644$ .

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

Paso 11.4

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

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Paso 11.4.1

El determinante de una matriz $2 \times 2$ puede obtenerse usando la fórmula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

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

Paso 11.4.2

Simplifica el determinante.

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Paso 11.4.2.1

Simplifica cada término.

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Paso 11.4.2.1.1

Multiplica $4.92$ por $48.24$ .

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

Paso 11.4.2.1.2

Multiplica $- 16.8$ por $20.84$ .

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

Paso 11.4.2.2

Resta $350.112$ de $237.3408$ .

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

Paso 11.5

Simplifica el determinante.

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Paso 11.5.1

Simplifica cada término.

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Paso 11.5.1.1

Multiplica $16$ por $669.2836$ .

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

Paso 11.5.1.2

Multiplica $- 8.915$ por $261.9312$ .

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

Paso 11.5.1.3

Multiplica $20$ por $- 112.7712$ .

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

Paso 11.5.2

Resta $2335.116648$ de $10708.5376$ .

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

Paso 11.5.3

Resta $2255.424$ de $8373.420952$ .

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

Paso 12

Simplifica el determinante.

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Paso 12.1

Simplifica cada término.

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Paso 12.1.1

Multiplica $24.915$ por $16265.59125187$ .

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

Paso 12.1.2

Multiplica $- 8.48$ por $6827.4524$ .

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

Paso 12.1.3

Multiplica $- 13$ por $- 12416.334875$ .

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

Paso 12.1.4

Multiplica $- 20.8$ por $6117.996952$ .

$405257.20604046 - 57896.796352 + 161412.353375 - 127254.3366016$

Paso 12.2

Resta $57896.796352$ de $405257.20604046$ .

$347360.40968846 + 161412.353375 - 127254.3366016$

Paso 12.3

Suma $347360.40968846$ y $161412.353375$ .

$508772.76306346 - 127254.3366016$

Paso 12.4

Resta $127254.3366016$ de $508772.76306346$ .

$381518.42646186$