Álgebra linear Exemplos

$[\begin{array}{c} 4 & 0 \\ 5 & 2 \end{array}] [\begin{array}{c} 3 & 7 \\ 1 & x \end{array}] = [\begin{array}{c} 12 & 28 \\ 17 & 69 \end{array}]$

Etapa 1

Multiplique $[\begin{array}{c} 4 & 0 \\ 5 & 2 \end{array}] [\begin{array}{c} 3 & 7 \\ 1 & x \end{array}]$ .

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Etapa 1.1

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 $2 \times 2$ .

Etapa 1.2

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

$[\begin{array}{c} 4 \cdot 3 + 0 \cdot 1 & 4 \cdot 7 + 0 x \\ 5 \cdot 3 + 2 \cdot 1 & 5 \cdot 7 + 2 x \end{array}] = [\begin{array}{c} 12 & 28 \\ 17 & 69 \end{array}]$

Etapa 1.3

Simplifique cada elemento da matriz multiplicando todas as expressões.

$[\begin{array}{c} 12 & 28 \\ 17 & 35 + 2 x \end{array}] = [\begin{array}{c} 12 & 28 \\ 17 & 69 \end{array}]$

Etapa 2

Write as a linear system of equations.

$12 = 12$

$28 = 28$

$17 = 17$

$35 + 2 x = 69$

Etapa 3

Since $17 = 17$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying $35 + 2 x = 69$ .