Question

Determine os valores de x e y de modo que a inversa da matriz
A=[x 3
1 0] seja a matriz
B=[0 1
y -2]

Obs: A e B são de ordem 2 A= x 3 1 0 B= 0 1 y -2

Answer 1

Boa noite

Devemos ter   $A*B= I_{2}$

Temos então

$A*B= \left[\begin{array}{ccc}x&3\\1&0\end{array}\right] * \left[\begin{array}{ccc}0&1\\y&-2\end{array}\right] = \\ \\ \\ \left[\begin{array}{ccc}x*0+3*y&x*1+3*(-2)\\1*0+0*y&1*1+0*(-2)\end{array}\right] \\ \\ \\ \left[\begin{array}{ccc}3y&x-6\\0&1\end{array}\right] = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right] \Rightarrow \left \{ {{3y=1} \atop {x-6=0}} \right. \\ \\ \\ 3y=1\Rightarrow \boxed{ y= \frac{1}{3} }\quad\quad e \quad\quad x-6=0\Rightarrow \boxed{ x=6}$