Matemática discreta Ejemplos

$0.5 [\begin{array}{c} 1 & 3 & 5 \\ 5 & 2 & - 1 \\ - 2 & 0 & 1 \end{array}] - 0.2 [\begin{array}{c} 2 & 3 & 4 \\ - 1 & 1 & - 4 \\ 3 & 5 & - 5 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1

Simplifica cada término.

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Paso 1.1

Multiplica $0.5$ por cada elemento de la matriz.

$[\begin{array}{c} 0.5 \cdot 1 & 0.5 \cdot 3 & 0.5 \cdot 5 \\ 0.5 \cdot 5 & 0.5 \cdot 2 & 0.5 \cdot - 1 \\ 0.5 \cdot - 2 & 0.5 \cdot 0 & 0.5 \cdot 1 \end{array}] - 0.2 [\begin{array}{c} 2 & 3 & 4 \\ - 1 & 1 & - 4 \\ 3 & 5 & - 5 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1.2

Simplifica cada elemento de la matriz.

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Paso 1.2.1

Multiplica $0.5$ por $1$ .

$[\begin{array}{c} 0.5 & 0.5 \cdot 3 & 0.5 \cdot 5 \\ 0.5 \cdot 5 & 0.5 \cdot 2 & 0.5 \cdot - 1 \\ 0.5 \cdot - 2 & 0.5 \cdot 0 & 0.5 \cdot 1 \end{array}] - 0.2 [\begin{array}{c} 2 & 3 & 4 \\ - 1 & 1 & - 4 \\ 3 & 5 & - 5 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1.2.2

Multiplica $0.5$ por $3$ .

$[\begin{array}{c} 0.5 & 1.5 & 0.5 \cdot 5 \\ 0.5 \cdot 5 & 0.5 \cdot 2 & 0.5 \cdot - 1 \\ 0.5 \cdot - 2 & 0.5 \cdot 0 & 0.5 \cdot 1 \end{array}] - 0.2 [\begin{array}{c} 2 & 3 & 4 \\ - 1 & 1 & - 4 \\ 3 & 5 & - 5 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1.2.3

Multiplica $0.5$ por $5$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 0.5 \cdot 5 & 0.5 \cdot 2 & 0.5 \cdot - 1 \\ 0.5 \cdot - 2 & 0.5 \cdot 0 & 0.5 \cdot 1 \end{array}] - 0.2 [\begin{array}{c} 2 & 3 & 4 \\ - 1 & 1 & - 4 \\ 3 & 5 & - 5 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1.2.4

Multiplica $0.5$ por $5$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 0.5 \cdot 2 & 0.5 \cdot - 1 \\ 0.5 \cdot - 2 & 0.5 \cdot 0 & 0.5 \cdot 1 \end{array}] - 0.2 [\begin{array}{c} 2 & 3 & 4 \\ - 1 & 1 & - 4 \\ 3 & 5 & - 5 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1.2.5

Multiplica $0.5$ por $2$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & 0.5 \cdot - 1 \\ 0.5 \cdot - 2 & 0.5 \cdot 0 & 0.5 \cdot 1 \end{array}] - 0.2 [\begin{array}{c} 2 & 3 & 4 \\ - 1 & 1 & - 4 \\ 3 & 5 & - 5 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1.2.6

Multiplica $0.5$ por $- 1$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ 0.5 \cdot - 2 & 0.5 \cdot 0 & 0.5 \cdot 1 \end{array}] - 0.2 [\begin{array}{c} 2 & 3 & 4 \\ - 1 & 1 & - 4 \\ 3 & 5 & - 5 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1.2.7

Multiplica $0.5$ por $- 2$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0.5 \cdot 0 & 0.5 \cdot 1 \end{array}] - 0.2 [\begin{array}{c} 2 & 3 & 4 \\ - 1 & 1 & - 4 \\ 3 & 5 & - 5 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1.2.8

Multiplica $0.5$ por $0$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \cdot 1 \end{array}] - 0.2 [\begin{array}{c} 2 & 3 & 4 \\ - 1 & 1 & - 4 \\ 3 & 5 & - 5 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1.2.9

Multiplica $0.5$ por $1$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] - 0.2 [\begin{array}{c} 2 & 3 & 4 \\ - 1 & 1 & - 4 \\ 3 & 5 & - 5 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1.3

Multiplica $- 0.2$ por cada elemento de la matriz.

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] + [\begin{array}{c} - 0.2 \cdot 2 & - 0.2 \cdot 3 & - 0.2 \cdot 4 \\ - 0.2 \cdot - 1 & - 0.2 \cdot 1 & - 0.2 \cdot - 4 \\ - 0.2 \cdot 3 & - 0.2 \cdot 5 & - 0.2 \cdot - 5 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1.4

Simplifica cada elemento de la matriz.

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Paso 1.4.1

Multiplica $- 0.2$ por $2$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] + [\begin{array}{c} - 0.4 & - 0.2 \cdot 3 & - 0.2 \cdot 4 \\ - 0.2 \cdot - 1 & - 0.2 \cdot 1 & - 0.2 \cdot - 4 \\ - 0.2 \cdot 3 & - 0.2 \cdot 5 & - 0.2 \cdot - 5 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1.4.2

Multiplica $- 0.2$ por $3$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] + [\begin{array}{c} - 0.4 & - 0.6 & - 0.2 \cdot 4 \\ - 0.2 \cdot - 1 & - 0.2 \cdot 1 & - 0.2 \cdot - 4 \\ - 0.2 \cdot 3 & - 0.2 \cdot 5 & - 0.2 \cdot - 5 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1.4.3

Multiplica $- 0.2$ por $4$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] + [\begin{array}{c} - 0.4 & - 0.6 & - 0.8 \\ - 0.2 \cdot - 1 & - 0.2 \cdot 1 & - 0.2 \cdot - 4 \\ - 0.2 \cdot 3 & - 0.2 \cdot 5 & - 0.2 \cdot - 5 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1.4.4

Multiplica $- 0.2$ por $- 1$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] + [\begin{array}{c} - 0.4 & - 0.6 & - 0.8 \\ 0.2 & - 0.2 \cdot 1 & - 0.2 \cdot - 4 \\ - 0.2 \cdot 3 & - 0.2 \cdot 5 & - 0.2 \cdot - 5 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1.4.5

Multiplica $- 0.2$ por $1$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] + [\begin{array}{c} - 0.4 & - 0.6 & - 0.8 \\ 0.2 & - 0.2 & - 0.2 \cdot - 4 \\ - 0.2 \cdot 3 & - 0.2 \cdot 5 & - 0.2 \cdot - 5 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1.4.6

Multiplica $- 0.2$ por $- 4$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] + [\begin{array}{c} - 0.4 & - 0.6 & - 0.8 \\ 0.2 & - 0.2 & 0.8 \\ - 0.2 \cdot 3 & - 0.2 \cdot 5 & - 0.2 \cdot - 5 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1.4.7

Multiplica $- 0.2$ por $3$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] + [\begin{array}{c} - 0.4 & - 0.6 & - 0.8 \\ 0.2 & - 0.2 & 0.8 \\ - 0.6 & - 0.2 \cdot 5 & - 0.2 \cdot - 5 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1.4.8

Multiplica $- 0.2$ por $5$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] + [\begin{array}{c} - 0.4 & - 0.6 & - 0.8 \\ 0.2 & - 0.2 & 0.8 \\ - 0.6 & - 1 & - 0.2 \cdot - 5 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1.4.9

Multiplica $- 0.2$ por $- 5$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] + [\begin{array}{c} - 0.4 & - 0.6 & - 0.8 \\ 0.2 & - 0.2 & 0.8 \\ - 0.6 & - 1 & 1 \end{array}] + 0.6 [\begin{array}{c} 3 & 4 & - 1 \\ 4 & 5 & 1 \\ 1 & 0 & 0 \end{array}]$

Paso 1.5

Multiplica $0.6$ por cada elemento de la matriz.

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] + [\begin{array}{c} - 0.4 & - 0.6 & - 0.8 \\ 0.2 & - 0.2 & 0.8 \\ - 0.6 & - 1 & 1 \end{array}] + [\begin{array}{c} 0.6 \cdot 3 & 0.6 \cdot 4 & 0.6 \cdot - 1 \\ 0.6 \cdot 4 & 0.6 \cdot 5 & 0.6 \cdot 1 \\ 0.6 \cdot 1 & 0.6 \cdot 0 & 0.6 \cdot 0 \end{array}]$

Paso 1.6

Simplifica cada elemento de la matriz.

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Paso 1.6.1

Multiplica $0.6$ por $3$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] + [\begin{array}{c} - 0.4 & - 0.6 & - 0.8 \\ 0.2 & - 0.2 & 0.8 \\ - 0.6 & - 1 & 1 \end{array}] + [\begin{array}{c} 1.8 & 0.6 \cdot 4 & 0.6 \cdot - 1 \\ 0.6 \cdot 4 & 0.6 \cdot 5 & 0.6 \cdot 1 \\ 0.6 \cdot 1 & 0.6 \cdot 0 & 0.6 \cdot 0 \end{array}]$

Paso 1.6.2

Multiplica $0.6$ por $4$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] + [\begin{array}{c} - 0.4 & - 0.6 & - 0.8 \\ 0.2 & - 0.2 & 0.8 \\ - 0.6 & - 1 & 1 \end{array}] + [\begin{array}{c} 1.8 & 2.4 & 0.6 \cdot - 1 \\ 0.6 \cdot 4 & 0.6 \cdot 5 & 0.6 \cdot 1 \\ 0.6 \cdot 1 & 0.6 \cdot 0 & 0.6 \cdot 0 \end{array}]$

Paso 1.6.3

Multiplica $0.6$ por $- 1$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] + [\begin{array}{c} - 0.4 & - 0.6 & - 0.8 \\ 0.2 & - 0.2 & 0.8 \\ - 0.6 & - 1 & 1 \end{array}] + [\begin{array}{c} 1.8 & 2.4 & - 0.6 \\ 0.6 \cdot 4 & 0.6 \cdot 5 & 0.6 \cdot 1 \\ 0.6 \cdot 1 & 0.6 \cdot 0 & 0.6 \cdot 0 \end{array}]$

Paso 1.6.4

Multiplica $0.6$ por $4$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] + [\begin{array}{c} - 0.4 & - 0.6 & - 0.8 \\ 0.2 & - 0.2 & 0.8 \\ - 0.6 & - 1 & 1 \end{array}] + [\begin{array}{c} 1.8 & 2.4 & - 0.6 \\ 2.4 & 0.6 \cdot 5 & 0.6 \cdot 1 \\ 0.6 \cdot 1 & 0.6 \cdot 0 & 0.6 \cdot 0 \end{array}]$

Paso 1.6.5

Multiplica $0.6$ por $5$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] + [\begin{array}{c} - 0.4 & - 0.6 & - 0.8 \\ 0.2 & - 0.2 & 0.8 \\ - 0.6 & - 1 & 1 \end{array}] + [\begin{array}{c} 1.8 & 2.4 & - 0.6 \\ 2.4 & 3 & 0.6 \cdot 1 \\ 0.6 \cdot 1 & 0.6 \cdot 0 & 0.6 \cdot 0 \end{array}]$

Paso 1.6.6

Multiplica $0.6$ por $1$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] + [\begin{array}{c} - 0.4 & - 0.6 & - 0.8 \\ 0.2 & - 0.2 & 0.8 \\ - 0.6 & - 1 & 1 \end{array}] + [\begin{array}{c} 1.8 & 2.4 & - 0.6 \\ 2.4 & 3 & 0.6 \\ 0.6 \cdot 1 & 0.6 \cdot 0 & 0.6 \cdot 0 \end{array}]$

Paso 1.6.7

Multiplica $0.6$ por $1$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] + [\begin{array}{c} - 0.4 & - 0.6 & - 0.8 \\ 0.2 & - 0.2 & 0.8 \\ - 0.6 & - 1 & 1 \end{array}] + [\begin{array}{c} 1.8 & 2.4 & - 0.6 \\ 2.4 & 3 & 0.6 \\ 0.6 & 0.6 \cdot 0 & 0.6 \cdot 0 \end{array}]$

Paso 1.6.8

Multiplica $0.6$ por $0$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] + [\begin{array}{c} - 0.4 & - 0.6 & - 0.8 \\ 0.2 & - 0.2 & 0.8 \\ - 0.6 & - 1 & 1 \end{array}] + [\begin{array}{c} 1.8 & 2.4 & - 0.6 \\ 2.4 & 3 & 0.6 \\ 0.6 & 0 & 0.6 \cdot 0 \end{array}]$

Paso 1.6.9

Multiplica $0.6$ por $0$ .

$[\begin{array}{c} 0.5 & 1.5 & 2.5 \\ 2.5 & 1 & - 0.5 \\ - 1 & 0 & 0.5 \end{array}] + [\begin{array}{c} - 0.4 & - 0.6 & - 0.8 \\ 0.2 & - 0.2 & 0.8 \\ - 0.6 & - 1 & 1 \end{array}] + [\begin{array}{c} 1.8 & 2.4 & - 0.6 \\ 2.4 & 3 & 0.6 \\ 0.6 & 0 & 0 \end{array}]$

Paso 2

Suma los elementos correspondientes.

$[\begin{array}{c} 0.5 - 0.4 & 1.5 - 0.6 & 2.5 - 0.8 \\ 2.5 + 0.2 & 1 - 0.2 & - 0.5 + 0.8 \\ - 1 - 0.6 & 0 - 1 & 0.5 + 1 \end{array}] + [\begin{array}{c} 1.8 & 2.4 & - 0.6 \\ 2.4 & 3 & 0.6 \\ 0.6 & 0 & 0 \end{array}]$

Paso 3

Simplify each element.

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Paso 3.1

Resta $0.4$ de $0.5$ .

$[\begin{array}{c} 0.1 & 1.5 - 0.6 & 2.5 - 0.8 \\ 2.5 + 0.2 & 1 - 0.2 & - 0.5 + 0.8 \\ - 1 - 0.6 & 0 - 1 & 0.5 + 1 \end{array}] + [\begin{array}{c} 1.8 & 2.4 & - 0.6 \\ 2.4 & 3 & 0.6 \\ 0.6 & 0 & 0 \end{array}]$

Paso 3.2

Resta $0.6$ de $1.5$ .

$[\begin{array}{c} 0.1 & 0.9 & 2.5 - 0.8 \\ 2.5 + 0.2 & 1 - 0.2 & - 0.5 + 0.8 \\ - 1 - 0.6 & 0 - 1 & 0.5 + 1 \end{array}] + [\begin{array}{c} 1.8 & 2.4 & - 0.6 \\ 2.4 & 3 & 0.6 \\ 0.6 & 0 & 0 \end{array}]$

Paso 3.3

Resta $0.8$ de $2.5$ .

$[\begin{array}{c} 0.1 & 0.9 & 1.7 \\ 2.5 + 0.2 & 1 - 0.2 & - 0.5 + 0.8 \\ - 1 - 0.6 & 0 - 1 & 0.5 + 1 \end{array}] + [\begin{array}{c} 1.8 & 2.4 & - 0.6 \\ 2.4 & 3 & 0.6 \\ 0.6 & 0 & 0 \end{array}]$

Paso 3.4

Suma $2.5$ y $0.2$ .

$[\begin{array}{c} 0.1 & 0.9 & 1.7 \\ 2.7 & 1 - 0.2 & - 0.5 + 0.8 \\ - 1 - 0.6 & 0 - 1 & 0.5 + 1 \end{array}] + [\begin{array}{c} 1.8 & 2.4 & - 0.6 \\ 2.4 & 3 & 0.6 \\ 0.6 & 0 & 0 \end{array}]$

Paso 3.5

Resta $0.2$ de $1$ .

$[\begin{array}{c} 0.1 & 0.9 & 1.7 \\ 2.7 & 0.8 & - 0.5 + 0.8 \\ - 1 - 0.6 & 0 - 1 & 0.5 + 1 \end{array}] + [\begin{array}{c} 1.8 & 2.4 & - 0.6 \\ 2.4 & 3 & 0.6 \\ 0.6 & 0 & 0 \end{array}]$

Paso 3.6

Suma $- 0.5$ y $0.8$ .

$[\begin{array}{c} 0.1 & 0.9 & 1.7 \\ 2.7 & 0.8 & 0.3 \\ - 1 - 0.6 & 0 - 1 & 0.5 + 1 \end{array}] + [\begin{array}{c} 1.8 & 2.4 & - 0.6 \\ 2.4 & 3 & 0.6 \\ 0.6 & 0 & 0 \end{array}]$

Paso 3.7

Resta $0.6$ de $- 1$ .

$[\begin{array}{c} 0.1 & 0.9 & 1.7 \\ 2.7 & 0.8 & 0.3 \\ - 1.6 & 0 - 1 & 0.5 + 1 \end{array}] + [\begin{array}{c} 1.8 & 2.4 & - 0.6 \\ 2.4 & 3 & 0.6 \\ 0.6 & 0 & 0 \end{array}]$

Paso 3.8

Resta $1$ de $0$ .

$[\begin{array}{c} 0.1 & 0.9 & 1.7 \\ 2.7 & 0.8 & 0.3 \\ - 1.6 & - 1 & 0.5 + 1 \end{array}] + [\begin{array}{c} 1.8 & 2.4 & - 0.6 \\ 2.4 & 3 & 0.6 \\ 0.6 & 0 & 0 \end{array}]$

Paso 3.9

Suma $0.5$ y $1$ .

$[\begin{array}{c} 0.1 & 0.9 & 1.7 \\ 2.7 & 0.8 & 0.3 \\ - 1.6 & - 1 & 1.5 \end{array}] + [\begin{array}{c} 1.8 & 2.4 & - 0.6 \\ 2.4 & 3 & 0.6 \\ 0.6 & 0 & 0 \end{array}]$

Paso 4

Suma los elementos correspondientes.

$[\begin{array}{c} 0.1 + 1.8 & 0.9 + 2.4 & 1.7 - 0.6 \\ 2.7 + 2.4 & 0.8 + 3 & 0.3 + 0.6 \\ - 1.6 + 0.6 & - 1 + 0 & 1.5 + 0 \end{array}]$

Paso 5

Simplify each element.

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Paso 5.1

Suma $0.1$ y $1.8$ .

$[\begin{array}{c} 1.9 & 0.9 + 2.4 & 1.7 - 0.6 \\ 2.7 + 2.4 & 0.8 + 3 & 0.3 + 0.6 \\ - 1.6 + 0.6 & - 1 + 0 & 1.5 + 0 \end{array}]$

Paso 5.2

Suma $0.9$ y $2.4$ .

$[\begin{array}{c} 1.9 & 3.3 & 1.7 - 0.6 \\ 2.7 + 2.4 & 0.8 + 3 & 0.3 + 0.6 \\ - 1.6 + 0.6 & - 1 + 0 & 1.5 + 0 \end{array}]$

Paso 5.3

Resta $0.6$ de $1.7$ .

$[\begin{array}{c} 1.9 & 3.3 & 1.1 \\ 2.7 + 2.4 & 0.8 + 3 & 0.3 + 0.6 \\ - 1.6 + 0.6 & - 1 + 0 & 1.5 + 0 \end{array}]$

Paso 5.4

Suma $2.7$ y $2.4$ .

$[\begin{array}{c} 1.9 & 3.3 & 1.1 \\ 5.1 & 0.8 + 3 & 0.3 + 0.6 \\ - 1.6 + 0.6 & - 1 + 0 & 1.5 + 0 \end{array}]$

Paso 5.5

Suma $0.8$ y $3$ .

$[\begin{array}{c} 1.9 & 3.3 & 1.1 \\ 5.1 & 3.8 & 0.3 + 0.6 \\ - 1.6 + 0.6 & - 1 + 0 & 1.5 + 0 \end{array}]$

Paso 5.6

Suma $0.3$ y $0.6$ .

$[\begin{array}{c} 1.9 & 3.3 & 1.1 \\ 5.1 & 3.8 & 0.9 \\ - 1.6 + 0.6 & - 1 + 0 & 1.5 + 0 \end{array}]$

Paso 5.7

Suma $- 1.6$ y $0.6$ .

$[\begin{array}{c} 1.9 & 3.3 & 1.1 \\ 5.1 & 3.8 & 0.9 \\ - 1 & - 1 + 0 & 1.5 + 0 \end{array}]$

Paso 5.8

Suma $- 1$ y $0$ .

$[\begin{array}{c} 1.9 & 3.3 & 1.1 \\ 5.1 & 3.8 & 0.9 \\ - 1 & - 1 & 1.5 + 0 \end{array}]$

Paso 5.9

Suma $1.5$ y $0$ .

$[\begin{array}{c} 1.9 & 3.3 & 1.1 \\ 5.1 & 3.8 & 0.9 \\ - 1 & - 1 & 1.5 \end{array}]$

Paso 6

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 6.1

Consider the corresponding sign chart.

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

Paso 6.2

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

Paso 6.3

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

$| \begin{array}{c} 3.8 & 0.9 \\ - 1 & 1.5 \end{array} |$

Paso 6.4

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

$1.9 | \begin{array}{c} 3.8 & 0.9 \\ - 1 & 1.5 \end{array} |$

Paso 6.5

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

$| \begin{array}{c} 5.1 & 0.9 \\ - 1 & 1.5 \end{array} |$

Paso 6.6

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

$- 3.3 | \begin{array}{c} 5.1 & 0.9 \\ - 1 & 1.5 \end{array} |$

Paso 6.7

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

$| \begin{array}{c} 5.1 & 3.8 \\ - 1 & - 1 \end{array} |$

Paso 6.8

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

$1.1 | \begin{array}{c} 5.1 & 3.8 \\ - 1 & - 1 \end{array} |$

Paso 6.9

Add the terms together.

$1.9 | \begin{array}{c} 3.8 & 0.9 \\ - 1 & 1.5 \end{array} | - 3.3 | \begin{array}{c} 5.1 & 0.9 \\ - 1 & 1.5 \end{array} | + 1.1 | \begin{array}{c} 5.1 & 3.8 \\ - 1 & - 1 \end{array} |$

Paso 7

Evalúa $| \begin{array}{c} 3.8 & 0.9 \\ - 1 & 1.5 \end{array} |$ .

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Paso 7.1

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

$1.9 (3.8 \cdot 1.5 - (- 1 \cdot 0.9)) - 3.3 | \begin{array}{c} 5.1 & 0.9 \\ - 1 & 1.5 \end{array} | + 1.1 | \begin{array}{c} 5.1 & 3.8 \\ - 1 & - 1 \end{array} |$

Paso 7.2

Simplifica el determinante.

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Paso 7.2.1

Simplifica cada término.

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Paso 7.2.1.1

Multiplica $3.8$ por $1.5$ .

$1.9 (5.7 - (- 1 \cdot 0.9)) - 3.3 | \begin{array}{c} 5.1 & 0.9 \\ - 1 & 1.5 \end{array} | + 1.1 | \begin{array}{c} 5.1 & 3.8 \\ - 1 & - 1 \end{array} |$

Paso 7.2.1.2

Multiplica $- (- 1 \cdot 0.9)$ .

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Paso 7.2.1.2.1

Multiplica $- 1$ por $0.9$ .

$1.9 (5.7 - - 0.9) - 3.3 | \begin{array}{c} 5.1 & 0.9 \\ - 1 & 1.5 \end{array} | + 1.1 | \begin{array}{c} 5.1 & 3.8 \\ - 1 & - 1 \end{array} |$

Paso 7.2.1.2.2

Multiplica $- 1$ por $- 0.9$ .

$1.9 (5.7 + 0.9) - 3.3 | \begin{array}{c} 5.1 & 0.9 \\ - 1 & 1.5 \end{array} | + 1.1 | \begin{array}{c} 5.1 & 3.8 \\ - 1 & - 1 \end{array} |$

Paso 7.2.2

Suma $5.7$ y $0.9$ .

$1.9 \cdot 6.6 - 3.3 | \begin{array}{c} 5.1 & 0.9 \\ - 1 & 1.5 \end{array} | + 1.1 | \begin{array}{c} 5.1 & 3.8 \\ - 1 & - 1 \end{array} |$

Paso 8

Evalúa $| \begin{array}{c} 5.1 & 0.9 \\ - 1 & 1.5 \end{array} |$ .

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Paso 8.1

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

$1.9 \cdot 6.6 - 3.3 (5.1 \cdot 1.5 - (- 1 \cdot 0.9)) + 1.1 | \begin{array}{c} 5.1 & 3.8 \\ - 1 & - 1 \end{array} |$

Paso 8.2

Simplifica el determinante.

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Paso 8.2.1

Simplifica cada término.

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Paso 8.2.1.1

Multiplica $5.1$ por $1.5$ .

$1.9 \cdot 6.6 - 3.3 (7.65 - (- 1 \cdot 0.9)) + 1.1 | \begin{array}{c} 5.1 & 3.8 \\ - 1 & - 1 \end{array} |$

Paso 8.2.1.2

Multiplica $- (- 1 \cdot 0.9)$ .

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Paso 8.2.1.2.1

Multiplica $- 1$ por $0.9$ .

$1.9 \cdot 6.6 - 3.3 (7.65 - - 0.9) + 1.1 | \begin{array}{c} 5.1 & 3.8 \\ - 1 & - 1 \end{array} |$

Paso 8.2.1.2.2

Multiplica $- 1$ por $- 0.9$ .

$1.9 \cdot 6.6 - 3.3 (7.65 + 0.9) + 1.1 | \begin{array}{c} 5.1 & 3.8 \\ - 1 & - 1 \end{array} |$

Paso 8.2.2

Suma $7.65$ y $0.9$ .

$1.9 \cdot 6.6 - 3.3 \cdot 8.55 + 1.1 | \begin{array}{c} 5.1 & 3.8 \\ - 1 & - 1 \end{array} |$

Paso 9

Evalúa $| \begin{array}{c} 5.1 & 3.8 \\ - 1 & - 1 \end{array} |$ .

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Paso 9.1

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

$1.9 \cdot 6.6 - 3.3 \cdot 8.55 + 1.1 (5.1 \cdot - 1 - (- 1 \cdot 3.8))$

Paso 9.2

Simplifica el determinante.

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Paso 9.2.1

Simplifica cada término.

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Paso 9.2.1.1

Multiplica $5.1$ por $- 1$ .

$1.9 \cdot 6.6 - 3.3 \cdot 8.55 + 1.1 (- 5.1 - (- 1 \cdot 3.8))$

Paso 9.2.1.2

Multiplica $- (- 1 \cdot 3.8)$ .

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Paso 9.2.1.2.1

Multiplica $- 1$ por $3.8$ .

$1.9 \cdot 6.6 - 3.3 \cdot 8.55 + 1.1 (- 5.1 - - 3.8)$

Paso 9.2.1.2.2

Multiplica $- 1$ por $- 3.8$ .

$1.9 \cdot 6.6 - 3.3 \cdot 8.55 + 1.1 (- 5.1 + 3.8)$

Paso 9.2.2

Suma $- 5.1$ y $3.8$ .

$1.9 \cdot 6.6 - 3.3 \cdot 8.55 + 1.1 \cdot - 1.3$

Paso 10

Simplifica el determinante.

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Paso 10.1

Simplifica cada término.

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Paso 10.1.1

Multiplica $1.9$ por $6.6$ .

$12.54 - 3.3 \cdot 8.55 + 1.1 \cdot - 1.3$

Paso 10.1.2

Multiplica $- 3.3$ por $8.55$ .

$12.54 - 28.215 + 1.1 \cdot - 1.3$

Paso 10.1.3

Multiplica $1.1$ por $- 1.3$ .

$12.54 - 28.215 - 1.43$

Paso 10.2

Resta $28.215$ de $12.54$ .

$- 15.675 - 1.43$

Paso 10.3

Resta $1.43$ de $- 15.675$ .

$- 17.105$