Question

pucamp. sejam as matrizes ....
o determinante da matriz A+B.C é
a)-4
b)-2
c)0
d)1
e)5

Answer 1

$A + (B*C)$

$\left[\begin{array}{ccc}0&1\\1&0\end{array}\right] + ( \left[\begin{array}{ccc}1&0\\2&1\end{array}\right] * \left[\begin{array}{ccc}1&2\\0&1\end{array}\right])$

$\left[\begin{array}{ccc}0&1\\1&0\end{array}\right] + \left[\begin{array}{ccc}1+0&2+0\\2+0&4+1\end{array}\right]$

$\left[\begin{array}{ccc}0&1\\1&0\end{array}\right] + \left[\begin{array}{ccc}1&2\\2&5\end{array}\right]$

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

Determinate = Produto da diagonal principal  - produto da diagonal secundária, ficaria:

$\boxed{5*1 - (3*3) =5 - 9 = -4 }$

LETRA A

Espero ter ajudado. :))