Question

Considere A=2 6 e B=1 5
0 -4 -2 -1
Calcule o det(x), onde o X é a matriz dada por:
7x-B=B-5(A-X).

a) -96
b) -76
c) -56
d) -26

Answer 1

Está desconfigurado mas acho que entendi. São matrizes 2x2, correto?

A= $\left[\begin{array}{ccc}2&6\\0&-4\end{array}\right]$

B=$\left[\begin{array}{ccc}1 &5\\-2&-1\end{array}\right]$

Pra achar det(x) vamos encontrar x, que é dado por:

7x-B=B-5(A-X)

7x-B=B-5A-5X

2X=2B-5X

2X= 2 $\left[\begin{array}{ccc}2&6\\0&-4\end{array}\right]$ - 5 B=$\left[\begin{array}{ccc}1&5\\-2&-1\end{array}\right]$

2X=  $\left[\begin{array}{ccc}2&10\\-4&-2\end{array}\right]$ - $\left[\begin{array}{ccc}10&30\\0&-20\end{array}\right]$

2X= $\left[\begin{array}{ccc}-8&-20\\-4&18\end{array}\right]$

X= $\left[\begin{array}{ccc}-4&-10\\-2&9\end{array}\right]$

det(x)= -36-20 = -56 (letra C)