Question

Dada as matrizes A = (aij)2x2 tal que a = {i+j se i = j // 0 se i ≠ j} e B = (bij)2x2 tal que b = 2i - 3j, então A + B igual a:

a)$\left[\begin{array}{ccc}-1&4\\-1&-2\end{array}\right]$
b)$\left[\begin{array}{ccc}1&-4\\-1&-2\end{array}\right]$
c)$\left[\begin{array}{ccc}-1&4\\1&2\end{array}\right]$
d)$\left[\begin{array}{ccc}1&-4\\1&2\end{array}\right]$
e)$\left[\begin{array}{ccc}1&4\\1&2\end{array}\right]$

Answer 1

$A=\left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right]\\\\\\ A=\left[\begin{array}{ccc}1+1&0\\0&2+2\end{array}\right]\\\\\\ A=\left[\begin{array}{ccc}2&0\\0&4\end{array}\right]\\\\\\\\ B=\left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right]\\\\\\ B=\left[\begin{array}{ccc}2-3&2-6\\4-3&4-6\end{array}\right]\\\\\\ B=\left[\begin{array}{ccc}-1&-4\\1&-2\end{array}\right]$


$A+B\\\\ \left[\begin{array}{ccc}2&0\\0&4\end{array}\right]+\left[\begin{array}{ccc}-1&-4\\1&-2\end{array}\right]\\\\\\ \left[\begin{array}{ccc}2+(-1)&0+(-4)\\0+1&4+(-2)\end{array}\right]\\\\\\ \left[\begin{array}{ccc}2-1&-4\\1&4-2\end{array}\right]\\\\\\ \left[\begin{array}{ccc}1&-4\\1&2\end{array}\right]$

Portanto, letra D.