Question

(UEL) A soma de todos os elementos da inversa da matriz
M=(1 -1
     (0  2)
é igual a:
a)-2
b)-1
c)0
d)1
e)2

Answer 1

$\left[\begin{array}{cc}1&-1\\0&2\end{array}\right] . \left[\begin{array}{cc}a&b\\c&d\end{array}\right]= \left[\begin{array}{cc}1&0\\0&1\end{array}\right] \\ \\ \left[\begin{array}{cc}a+0&b-d\\0+2c&0+2d\end{array}\right] = \left[\begin{array}{cc}1&0\\0&1\end{array}\right] \\ \\ a=1 \\ 2c=0 /c=0 \\ 2d=1 / d= \frac{1}{2} \\ \\ b-d=0/b- \frac{1}{2}=0/b= \frac{1}{2} \\ \\ \\ \\ \\ a+b+c+d= \\ 1+ \frac{1}{2} +0+ \frac{1}{2}= 2$