Question

Considere as matrizes com x, y, z números reais. Se A.B =C, a soma dos elementos da matriz A é:
a) 9
b) 40
c) 41
d) 50
e) 81.

Answer 1

Devemos realizar o produto das matrizes A e B. Assim:

$A\times B= \left(\begin{array}{cc}1& x\\y& z\end{array}\right)\times \left(\begin{array}{cc}1&2\\1&1\end{array}\right)\\\\ C=\left(\begin{array}{cc} 1\times1+x\times 1& 1\times2+x\times1\\y\times1+z\times1 & y\times2+z\times1\end{array}\right)\\\\ \left(\begin{array}{cc}4& 5\\36& 45\end{array}\right)=\left(\begin{array}{cc} 1+x& 2+x\\y+z & 2y+z\end{array}\right)\\\\ \boxed{x=3}~~\boxed{y=9}~~\boxed{z=27}$

Desse modo, a soma dos elementos da matriz A é:

$Soma=1+x+y+z=1+3+9+27\\\\ \boxed{Soma=40}\Longrightarrow Letra~B$