Álgebra linear Exemplos

$[\begin{array}{c} 0.3 & 0.2 & 0.3 \\ 0.4 & 0.3 & 0.3 \\ 0.3 & 0.3 & 0.2 \end{array}] - [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}] \cdot [\begin{array}{c} 81 \\ 8 \\ 9 \end{array}]$

Etapa 1

Multiplique $- 1$ por cada elemento da matriz.

$[\begin{array}{c} 0.3 & 0.2 & 0.3 \\ 0.4 & 0.3 & 0.3 \\ 0.3 & 0.3 & 0.2 \end{array}] + [\begin{array}{c} - 1 \cdot 1 & - 0 & - 0 \\ - 0 & - 1 \cdot 1 & - 0 \\ - 0 & - 0 & - 1 \cdot 1 \end{array}] \cdot [\begin{array}{c} 81 \\ 8 \\ 9 \end{array}]$

Etapa 2

Simplifique cada elemento da matriz.

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Etapa 2.1

Multiplique $- 1$ por $1$ .

$[\begin{array}{c} 0.3 & 0.2 & 0.3 \\ 0.4 & 0.3 & 0.3 \\ 0.3 & 0.3 & 0.2 \end{array}] + [\begin{array}{c} - 1 & - 0 & - 0 \\ - 0 & - 1 \cdot 1 & - 0 \\ - 0 & - 0 & - 1 \cdot 1 \end{array}] \cdot [\begin{array}{c} 81 \\ 8 \\ 9 \end{array}]$

Etapa 2.2

Multiplique $- 1$ por $0$ .

$[\begin{array}{c} 0.3 & 0.2 & 0.3 \\ 0.4 & 0.3 & 0.3 \\ 0.3 & 0.3 & 0.2 \end{array}] + [\begin{array}{c} - 1 & 0 & - 0 \\ - 0 & - 1 \cdot 1 & - 0 \\ - 0 & - 0 & - 1 \cdot 1 \end{array}] \cdot [\begin{array}{c} 81 \\ 8 \\ 9 \end{array}]$

Etapa 2.3

Multiplique $- 1$ por $0$ .

$[\begin{array}{c} 0.3 & 0.2 & 0.3 \\ 0.4 & 0.3 & 0.3 \\ 0.3 & 0.3 & 0.2 \end{array}] + [\begin{array}{c} - 1 & 0 & 0 \\ - 0 & - 1 \cdot 1 & - 0 \\ - 0 & - 0 & - 1 \cdot 1 \end{array}] \cdot [\begin{array}{c} 81 \\ 8 \\ 9 \end{array}]$

Etapa 2.4

Multiplique $- 1$ por $0$ .

$[\begin{array}{c} 0.3 & 0.2 & 0.3 \\ 0.4 & 0.3 & 0.3 \\ 0.3 & 0.3 & 0.2 \end{array}] + [\begin{array}{c} - 1 & 0 & 0 \\ 0 & - 1 \cdot 1 & - 0 \\ - 0 & - 0 & - 1 \cdot 1 \end{array}] \cdot [\begin{array}{c} 81 \\ 8 \\ 9 \end{array}]$

Etapa 2.5

Multiplique $- 1$ por $1$ .

$[\begin{array}{c} 0.3 & 0.2 & 0.3 \\ 0.4 & 0.3 & 0.3 \\ 0.3 & 0.3 & 0.2 \end{array}] + [\begin{array}{c} - 1 & 0 & 0 \\ 0 & - 1 & - 0 \\ - 0 & - 0 & - 1 \cdot 1 \end{array}] \cdot [\begin{array}{c} 81 \\ 8 \\ 9 \end{array}]$

Etapa 2.6

Multiplique $- 1$ por $0$ .

$[\begin{array}{c} 0.3 & 0.2 & 0.3 \\ 0.4 & 0.3 & 0.3 \\ 0.3 & 0.3 & 0.2 \end{array}] + [\begin{array}{c} - 1 & 0 & 0 \\ 0 & - 1 & 0 \\ - 0 & - 0 & - 1 \cdot 1 \end{array}] \cdot [\begin{array}{c} 81 \\ 8 \\ 9 \end{array}]$

Etapa 2.7

Multiplique $- 1$ por $0$ .

$[\begin{array}{c} 0.3 & 0.2 & 0.3 \\ 0.4 & 0.3 & 0.3 \\ 0.3 & 0.3 & 0.2 \end{array}] + [\begin{array}{c} - 1 & 0 & 0 \\ 0 & - 1 & 0 \\ 0 & - 0 & - 1 \cdot 1 \end{array}] \cdot [\begin{array}{c} 81 \\ 8 \\ 9 \end{array}]$

Etapa 2.8

Multiplique $- 1$ por $0$ .

$[\begin{array}{c} 0.3 & 0.2 & 0.3 \\ 0.4 & 0.3 & 0.3 \\ 0.3 & 0.3 & 0.2 \end{array}] + [\begin{array}{c} - 1 & 0 & 0 \\ 0 & - 1 & 0 \\ 0 & 0 & - 1 \cdot 1 \end{array}] \cdot [\begin{array}{c} 81 \\ 8 \\ 9 \end{array}]$

Etapa 2.9

Multiplique $- 1$ por $1$ .

$[\begin{array}{c} 0.3 & 0.2 & 0.3 \\ 0.4 & 0.3 & 0.3 \\ 0.3 & 0.3 & 0.2 \end{array}] + [\begin{array}{c} - 1 & 0 & 0 \\ 0 & - 1 & 0 \\ 0 & 0 & - 1 \end{array}] \cdot [\begin{array}{c} 81 \\ 8 \\ 9 \end{array}]$

Etapa 3

Multiplique $[\begin{array}{c} - 1 & 0 & 0 \\ 0 & - 1 & 0 \\ 0 & 0 & - 1 \end{array}] [\begin{array}{c} 81 \\ 8 \\ 9 \end{array}]$ .

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Etapa 3.1

Duas matrizes podem ser multiplicadas se e somente se o número de colunas da primeira matriz for igual ao número de linhas da segunda matriz. Nesse caso, a primeira matriz é $3 \times 3$ e a segunda matriz é $3 \times 1$ .

Etapa 3.2

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

$[\begin{array}{c} 0.3 & 0.2 & 0.3 \\ 0.4 & 0.3 & 0.3 \\ 0.3 & 0.3 & 0.2 \end{array}] + [\begin{array}{c} - 1 \cdot 81 + 0 \cdot 8 + 0 \cdot 9 \\ 0 \cdot 81 - 1 \cdot 8 + 0 \cdot 9 \\ 0 \cdot 81 + 0 \cdot 8 - 1 \cdot 9 \end{array}]$

Etapa 3.3

Simplifique cada elemento da matriz multiplicando todas as expressões.

$[\begin{array}{c} 0.3 & 0.2 & 0.3 \\ 0.4 & 0.3 & 0.3 \\ 0.3 & 0.3 & 0.2 \end{array}] + [\begin{array}{c} - 81 \\ - 8 \\ - 9 \end{array}]$