Question

ME AJUDEEEEM

*VALENDO MELHOR RESPOSTA E 80 PONTOS*

Answer 1

Resposta:

a) $\left[\begin{array}{cc}6&5\\7&1\end{array}\right]$

b) $\left[\begin{array}{cc}5&4\\5&-1\end{array}\right]$

c) $\left[\begin{array}{cc}7&1\\12&-2\end{array}\right]$

d) $\left[\begin{array}{cc}9&5\\12&-1\end{array}\right]$

Explicação passo a passo:

O exercício pede soma de matrizes, ou seja, devemos somar os elementos das matrizes que estejam nas mesmas posições (mesma linha e mesma coluna). Atente-se à regra de sinal, pois irão aparecer somas envolvendo números negativos nos itens b, c e d.

Temos as matrizes a seguir:

A = $\left[\begin{array}{cc}2&4\\0&1\end{array}\right]$

B = $\left[\begin{array}{cc}4&1\\7&0\end{array}\right]$

C = $\left[\begin{array}{cc}3&0\\5&-2\end{array}\right]$

Agora vamos realizar as somas, nos atentando a somarmos os elementos de mesma posição entre as matrizes:

a) A + B = $\left[\begin{array}{cc}2&4\\0&1\end{array}\right]$ + $\left[\begin{array}{cc}4&1\\7&0\end{array}\right]$ = $\left[\begin{array}{cc}2+4&4+1\\0+7&1+0\end{array}\right]$ = $\left[\begin{array}{cc}6&5\\7&1\end{array}\right]$

b) A + C = $\left[\begin{array}{cc}2&4\\0&1\end{array}\right]$ + $\left[\begin{array}{cc}3&0\\5&-2\end{array}\right]$ = $\left[\begin{array}{cc}2+3&4+0\\0+5&1+(-2)\end{array}\right]$ =

= $\left[\begin{array}{cc}2+3&4+0\\0+5&1-2\end{array}\right]$ = $\left[\begin{array}{cc}5&4\\5&-1\end{array}\right]$

c) B + C = $\left[\begin{array}{cc}4&1\\7&0\end{array}\right]$ + $\left[\begin{array}{cc}3&0\\5&-2\end{array}\right]$ = $\left[\begin{array}{cc}4+3&1+0\\7+5&0+(-2)\end{array}\right]$ = $\left[\begin{array}{cc}7&1\\12&-2\end{array}\right]$

d) A + B + C = $\left[\begin{array}{cc}2&4\\0&1\end{array}\right]$ + $\left[\begin{array}{cc}4&1\\7&0\end{array}\right]$ + $\left[\begin{array}{cc}3&0\\5&-2\end{array}\right]$ = $\left[\begin{array}{cc}2+4+3&4+1+0\\0+7+5&1+0+(-2)\end{array}\right]$ =

= $\left[\begin{array}{cc}2+4+3&4+1+0\\0+7+5&1+0-2\end{array}\right]$ = $\left[\begin{array}{cc}9&5\\12&-1\end{array}\right]$