Matemática discreta Exemplos

$[\begin{array}{c} - 0.12 & - 0.02 & 0.18 \\ 0 & 0.1 & - 0.3 \\ 0.06 & - 0.14 & 0.06 \end{array}] \cdot - 0.06$

Etapa 1

Mova $- 0.06$ para a esquerda de $[\begin{array}{c} - 0.12 & - 0.02 & 0.18 \\ 0 & 0.1 & - 0.3 \\ 0.06 & - 0.14 & 0.06 \end{array}]$ .

$- 0.06 \cdot [\begin{array}{c} - 0.12 & - 0.02 & 0.18 \\ 0 & 0.1 & - 0.3 \\ 0.06 & - 0.14 & 0.06 \end{array}]$

Etapa 2

Multiplique $- 0.06$ por cada elemento da matriz.

$[\begin{array}{c} - 0.06 \cdot - 0.12 & - 0.06 \cdot - 0.02 & - 0.06 \cdot 0.18 \\ - 0.06 \cdot 0 & - 0.06 \cdot 0.1 & - 0.06 \cdot - 0.3 \\ - 0.06 \cdot 0.06 & - 0.06 \cdot - 0.14 & - 0.06 \cdot 0.06 \end{array}]$

Etapa 3

Simplifique cada elemento da matriz.

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Etapa 3.1

Multiplique $- 0.06$ por $- 0.12$ .

$[\begin{array}{c} 0.0072 & - 0.06 \cdot - 0.02 & - 0.06 \cdot 0.18 \\ - 0.06 \cdot 0 & - 0.06 \cdot 0.1 & - 0.06 \cdot - 0.3 \\ - 0.06 \cdot 0.06 & - 0.06 \cdot - 0.14 & - 0.06 \cdot 0.06 \end{array}]$

Etapa 3.2

Multiplique $- 0.06$ por $- 0.02$ .

$[\begin{array}{c} 0.0072 & 0.0012 & - 0.06 \cdot 0.18 \\ - 0.06 \cdot 0 & - 0.06 \cdot 0.1 & - 0.06 \cdot - 0.3 \\ - 0.06 \cdot 0.06 & - 0.06 \cdot - 0.14 & - 0.06 \cdot 0.06 \end{array}]$

Etapa 3.3

Multiplique $- 0.06$ por $0.18$ .

$[\begin{array}{c} 0.0072 & 0.0012 & - 0.0108 \\ - 0.06 \cdot 0 & - 0.06 \cdot 0.1 & - 0.06 \cdot - 0.3 \\ - 0.06 \cdot 0.06 & - 0.06 \cdot - 0.14 & - 0.06 \cdot 0.06 \end{array}]$

Etapa 3.4

Multiplique $- 0.06$ por $0$ .

$[\begin{array}{c} 0.0072 & 0.0012 & - 0.0108 \\ 0 & - 0.06 \cdot 0.1 & - 0.06 \cdot - 0.3 \\ - 0.06 \cdot 0.06 & - 0.06 \cdot - 0.14 & - 0.06 \cdot 0.06 \end{array}]$

Etapa 3.5

Multiplique $- 0.06$ por $0.1$ .

$[\begin{array}{c} 0.0072 & 0.0012 & - 0.0108 \\ 0 & - 0.006 & - 0.06 \cdot - 0.3 \\ - 0.06 \cdot 0.06 & - 0.06 \cdot - 0.14 & - 0.06 \cdot 0.06 \end{array}]$

Etapa 3.6

Multiplique $- 0.06$ por $- 0.3$ .

$[\begin{array}{c} 0.0072 & 0.0012 & - 0.0108 \\ 0 & - 0.006 & 0.018 \\ - 0.06 \cdot 0.06 & - 0.06 \cdot - 0.14 & - 0.06 \cdot 0.06 \end{array}]$

Etapa 3.7

Multiplique $- 0.06$ por $0.06$ .

$[\begin{array}{c} 0.0072 & 0.0012 & - 0.0108 \\ 0 & - 0.006 & 0.018 \\ - 0.0036 & - 0.06 \cdot - 0.14 & - 0.06 \cdot 0.06 \end{array}]$

Etapa 3.8

Multiplique $- 0.06$ por $- 0.14$ .

$[\begin{array}{c} 0.0072 & 0.0012 & - 0.0108 \\ 0 & - 0.006 & 0.018 \\ - 0.0036 & 0.0084 & - 0.06 \cdot 0.06 \end{array}]$

Etapa 3.9

Multiplique $- 0.06$ por $0.06$ .

$[\begin{array}{c} 0.0072 & 0.0012 & - 0.0108 \\ 0 & - 0.006 & 0.018 \\ - 0.0036 & 0.0084 & - 0.0036 \end{array}]$

Etapa 4

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 column $1$ by its cofactor and add.

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Etapa 4.1

Consider the corresponding sign chart.

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

Etapa 4.2

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

Etapa 4.3

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

$| \begin{array}{c} - 0.006 & 0.018 \\ 0.0084 & - 0.0036 \end{array} |$

Etapa 4.4

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

$0.0072 | \begin{array}{c} - 0.006 & 0.018 \\ 0.0084 & - 0.0036 \end{array} |$

Etapa 4.5

The minor for $a_{21}$ is the determinant with row $2$ and column $1$ deleted.

$| \begin{array}{c} 0.0012 & - 0.0108 \\ 0.0084 & - 0.0036 \end{array} |$

Etapa 4.6

Multiply element $a_{21}$ by its cofactor.

$0 | \begin{array}{c} 0.0012 & - 0.0108 \\ 0.0084 & - 0.0036 \end{array} |$

Etapa 4.7

The minor for $a_{31}$ is the determinant with row $3$ and column $1$ deleted.

$| \begin{array}{c} 0.0012 & - 0.0108 \\ - 0.006 & 0.018 \end{array} |$

Etapa 4.8

Multiply element $a_{31}$ by its cofactor.

$- 0.0036 | \begin{array}{c} 0.0012 & - 0.0108 \\ - 0.006 & 0.018 \end{array} |$

Etapa 4.9

Add the terms together.

$0.0072 | \begin{array}{c} - 0.006 & 0.018 \\ 0.0084 & - 0.0036 \end{array} | + 0 | \begin{array}{c} 0.0012 & - 0.0108 \\ 0.0084 & - 0.0036 \end{array} | - 0.0036 | \begin{array}{c} 0.0012 & - 0.0108 \\ - 0.006 & 0.018 \end{array} |$

Etapa 5

Multiplique $0$ por $| \begin{array}{c} 0.0012 & - 0.0108 \\ 0.0084 & - 0.0036 \end{array} |$ .

$0.0072 | \begin{array}{c} - 0.006 & 0.018 \\ 0.0084 & - 0.0036 \end{array} | + 0 - 0.0036 | \begin{array}{c} 0.0012 & - 0.0108 \\ - 0.006 & 0.018 \end{array} |$

Etapa 6

Avalie $| \begin{array}{c} - 0.006 & 0.018 \\ 0.0084 & - 0.0036 \end{array} |$ .

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Etapa 6.1

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

$0.0072 (- 0.006 \cdot - 0.0036 - 0.0084 \cdot 0.018) + 0 - 0.0036 | \begin{array}{c} 0.0012 & - 0.0108 \\ - 0.006 & 0.018 \end{array} |$

Etapa 6.2

Simplifique o determinante.

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Etapa 6.2.1

Simplifique cada termo.

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Etapa 6.2.1.1

Multiplique $- 0.006$ por $- 0.0036$ .

$0.0072 (0.0000216 - 0.0084 \cdot 0.018) + 0 - 0.0036 | \begin{array}{c} 0.0012 & - 0.0108 \\ - 0.006 & 0.018 \end{array} |$

Etapa 6.2.1.2

Multiplique $- 0.0084$ por $0.018$ .

$0.0072 (0.0000216 - 0.0001512) + 0 - 0.0036 | \begin{array}{c} 0.0012 & - 0.0108 \\ - 0.006 & 0.018 \end{array} |$

Etapa 6.2.2

Subtraia $0.0001512$ de $0.0000216$ .

$0.0072 \cdot - 0.0001296 + 0 - 0.0036 | \begin{array}{c} 0.0012 & - 0.0108 \\ - 0.006 & 0.018 \end{array} |$

Etapa 7

Avalie $| \begin{array}{c} 0.0012 & - 0.0108 \\ - 0.006 & 0.018 \end{array} |$ .

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Etapa 7.1

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

$0.0072 \cdot - 0.0001296 + 0 - 0.0036 (0.0012 \cdot 0.018 - (- 0.006 \cdot - 0.0108))$

Etapa 7.2

Simplifique o determinante.

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Etapa 7.2.1

Simplifique cada termo.

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Etapa 7.2.1.1

Multiplique $0.0012$ por $0.018$ .

$0.0072 \cdot - 0.0001296 + 0 - 0.0036 (0.0000216 - (- 0.006 \cdot - 0.0108))$

Etapa 7.2.1.2

Multiplique $- (- 0.006 \cdot - 0.0108)$ .

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Etapa 7.2.1.2.1

Multiplique $- 0.006$ por $- 0.0108$ .

$0.0072 \cdot - 0.0001296 + 0 - 0.0036 (0.0000216 - 1 \cdot 0.0000648)$

Etapa 7.2.1.2.2

Multiplique $- 1$ por $0.0000648$ .

$0.0072 \cdot - 0.0001296 + 0 - 0.0036 (0.0000216 - 0.0000648)$

Etapa 7.2.2

Subtraia $0.0000648$ de $0.0000216$ .

$0.0072 \cdot - 0.0001296 + 0 - 0.0036 \cdot - 0.0000432$

Etapa 8

Simplifique o determinante.

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Etapa 8.1

Simplifique cada termo.

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Etapa 8.1.1

Multiplique $0.0072$ por $- 0.0001296$ .

$- 0.00000093 + 0 - 0.0036 \cdot - 0.0000432$

Etapa 8.1.2

Multiplique $- 0.0036$ por $- 0.0000432$ .

$- 0.00000093 + 0 + 0.00000015$

Etapa 8.2

Some $- 0.00000093$ e $0$ .

$- 0.00000093 + 0.00000015$

Etapa 8.3

Some $- 0.00000093$ e $0.00000015$ .

$- 0.000000\overline{7}$