Question

(PUC–SP–Adaptada) São dadas as matrizes A = (aij) e B = (bij), quadradas de ordem 2, com aij = 3i + 4j e bij = – 4i – j. Considerando C = A + B, calcule a matriz C.

Answer 1

Resposta:

Leia abaixo

Explicação passo-a-passo:

$A_{2,2}\: \: \: \: a_{ij} = 3i + 4j$

$A = \large\mathsf{\begin{vmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{vmatrix}} = \large\mathsf{\begin{vmatrix}(3)(1) + (4)(1)&(3)(1) + (4)(2)\\(3)(2) + (4)(1)&(3)(2) +(4)(2)\end{vmatrix}} = \large\mathsf{\begin{vmatrix}7&11\\10&14\end{vmatrix}}$

$B_{2,2}\: \: \: \: b_{ij} = -4i$

$B = \large\mathsf{\begin{vmatrix}b_{11}&b_{12}\\b_{21}&b_{22}\end{vmatrix}} = \large\mathsf{\begin{vmatrix}(-4)(1)&(-4)(1)\\(-4)(2)&(-4)(2)\end{vmatrix}} = \large\mathsf{\begin{vmatrix}-4&-4\\-8&-8\end{vmatrix}}$

$A + B = \large\mathsf{\begin{vmatrix}7&11\\10&14\end{vmatrix}} + \large\mathsf{\begin{vmatrix}-4&-4\\-8&-8\end{vmatrix}} = \large\mathsf{\begin{vmatrix}3&7\\2&6\end{vmatrix}}$