Pré-cálculo Exemplos

$[\begin{array}{c} \cos (\frac{π}{2}) & - \sin (\frac{π}{2}) \\ \sin (\frac{π}{2}) & \cos (\frac{π}{2}) \end{array}] [\begin{array}{c} 0 & 9 & 0 & 10 \\ 8 & 7 & 0 & 0 \end{array}]$

Etapa 1

O valor exato de $\cos (\frac{π}{2})$ é $0$ .

$[\begin{array}{c} 0 & - \sin (\frac{π}{2}) \\ \sin (\frac{π}{2}) & \cos (\frac{π}{2}) \end{array}] [\begin{array}{c} 0 & 9 & 0 & 10 \\ 8 & 7 & 0 & 0 \end{array}]$

Etapa 2

O valor exato de $\sin (\frac{π}{2})$ é $1$ .

$[\begin{array}{c} 0 & - 1 \cdot 1 \\ \sin (\frac{π}{2}) & \cos (\frac{π}{2}) \end{array}] [\begin{array}{c} 0 & 9 & 0 & 10 \\ 8 & 7 & 0 & 0 \end{array}]$

Etapa 3

Multiplique $- 1$ por $1$ .

$[\begin{array}{c} 0 & - 1 \\ \sin (\frac{π}{2}) & \cos (\frac{π}{2}) \end{array}] [\begin{array}{c} 0 & 9 & 0 & 10 \\ 8 & 7 & 0 & 0 \end{array}]$

Etapa 4

O valor exato de $\sin (\frac{π}{2})$ é $1$ .

$[\begin{array}{c} 0 & - 1 \\ 1 & \cos (\frac{π}{2}) \end{array}] [\begin{array}{c} 0 & 9 & 0 & 10 \\ 8 & 7 & 0 & 0 \end{array}]$

Etapa 5

O valor exato de $\cos (\frac{π}{2})$ é $0$ .

$[\begin{array}{c} 0 & - 1 \\ 1 & 0 \end{array}] [\begin{array}{c} 0 & 9 & 0 & 10 \\ 8 & 7 & 0 & 0 \end{array}]$

Etapa 6

Multiplique $[\begin{array}{c} 0 & - 1 \\ 1 & 0 \end{array}] [\begin{array}{c} 0 & 9 & 0 & 10 \\ 8 & 7 & 0 & 0 \end{array}]$ .

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Etapa 6.1

Two matrices can be multiplied if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. In this case, the first matrix is $2 \times 2$ and the second matrix is $2 \times 4$ .

Etapa 6.2

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

$[\begin{array}{c} 0 \cdot 0 - 1 \cdot 8 & 0 \cdot 9 - 1 \cdot 7 & 0 \cdot 0 - 0 & 0 \cdot 10 - 0 \\ 1 \cdot 0 + 0 \cdot 8 & 1 \cdot 9 + 0 \cdot 7 & 1 \cdot 0 + 0 \cdot 0 & 1 \cdot 10 + 0 \cdot 0 \end{array}]$

Etapa 6.3

Simplifique cada elemento da matriz multiplicando todas as expressões.

$[\begin{array}{c} - 8 & - 7 & 0 & 0 \\ 0 & 9 & 0 & 10 \end{array}]$