Question

Considerando as matrizes

Answer 1

Oii!

A soma e a subtração entre matrizes só é possível se as matrizes que estiverem envolvidas nessas operações tiverem as mesmas dimensões, o que não vai ser um problema nessa situação. Todas as matrizes na primeira questão são de ordem 2, e todas as matrizes da segunda questão são de ordem 3.

A soma e a subtração entre matrizes é feita de elemento com seu elemento correspondente.

Ex:

$\left[\begin{array}{cc}1&2\\4&5\\7&8\end{array}\right]$ + $\left[\begin{array}{cc}2&1\\5&4\\8&7\end{array}\right]$ = $\left[\begin{array}{cc}1+2&2+1\\4+5&5+4\\7+8&8+7\end{array}\right]$ = $\left[\begin{array}{cc}3&3\\9&9\\15&15\end{array}\right]$

Isto é, elemento a11 com elemento a11, elemento a12 com elemento a12, etc.

Portanto, vamos lá,

1.

A = $\left[\begin{array}{cc}2&4\\3&0\end{array}\right]$   B = $\left[\begin{array}{cc}-1&3\\4&7\end{array}\right]$   C = $\left[\begin{array}{cc}0&2\\5&8\end{array}\right]$

a)

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

b)

A + C = $\left[\begin{array}{cc}2&4\\3&0\end{array}\right]$ + $\left[\begin{array}{cc}0&2\\5&8\end{array}\right]$ = $\left[\begin{array}{cc}2+0&4+2\\3+5&0+8\end{array}\right]$ = $\left[\begin{array}{cc}2&6\\8&8\end{array}\right]$

c)

B - C = $\left[\begin{array}{cc}-1&3\\4&7\end{array}\right]$ - $\left[\begin{array}{cc}0&2\\5&8\end{array}\right]$ = $\left[\begin{array}{cc}-1-0&3-2\\4-5&7-8\end{array}\right]$ = $\left[\begin{array}{cc}-1&1\\-1&-1\end{array}\right]$

d)

B + C - A = $\left[\begin{array}{cc}-1&3\\4&7\end{array}\right]$ + $\left[\begin{array}{cc}0&2\\5&8\end{array}\right]$ - $\left[\begin{array}{cc}2&4\\3&0\end{array}\right]$ = $\left[\begin{array}{cc}-1+0-2&3+2-4\\4+5-3&7+8-0\end{array}\right]$ =

$\left[\begin{array}{cc}-3&1\\6&15\end{array}\right]$

2.

A = $\left[\begin{array}{ccc}3&1&0\\-1&2&4\\5&1&2\end{array}\right]$   B = $\left[\begin{array}{ccc}1&0&3\\2&-1&2\\3&2&8\end{array}\right]$   C = $\left[\begin{array}{ccc}0&1&0\\2&9&6\\5&1&-3\end{array}\right]$

a)

A + B = $\left[\begin{array}{ccc}3&1&0\\-1&2&4\\5&1&2\end{array}\right]$ + $\left[\begin{array}{ccc}1&0&3\\2&-1&2\\3&2&8\end{array}\right]$ = $\left[\begin{array}{ccc}3+1&1+0&0+3\\-1+2&2-1&4+2\\5+3&1+2&2+8\end{array}\right]$ =

$\left[\begin{array}{ccc}4&1&3\\1&1&6\\8&3&10\end{array}\right]$

b)

A - B = $\left[\begin{array}{ccc}3&1&0\\-1&2&4\\5&1&2\end{array}\right]$ - $\left[\begin{array}{ccc}1&0&3\\2&-1&2\\3&2&8\end{array}\right]$ = $\left[\begin{array}{ccc}3-1&1-0&0-3\\-1-2&2+1&4-2\\5-3&1-2&2-8\end{array}\right]$ =

$\left[\begin{array}{ccc}2&1&-3\\-3&3&2\\2&-1&-6\end{array}\right]$

c)

C + A - B = $\left[\begin{array}{ccc}0&1&0\\2&9&6\\5&1&-3\end{array}\right]$ + $\left[\begin{array}{ccc}3&1&0\\-1&2&4\\5&1&2\end{array}\right]$ - $\left[\begin{array}{ccc}1&0&3\\2&-1&2\\3&2&8\end{array}\right]$ =

$\left[\begin{array}{ccc}0+3-1&1+1-0&0+0-3\\2-1-2&9+2+1&6+4-2\\5+5-3&1+1-2&-3+2-8\end{array}\right]$ = $\left[\begin{array}{ccc}2&2&-3\\-1&12&8\\7&0&-9\end{array}\right]$