Solve the following equations
Question:

If $\left[\begin{array}{cc}x y & 4 \\ z+6 & x+y\end{array}\right]=\left[\begin{array}{cc}8 & w \\ 0 & 6\end{array}\right]$, then find the values of $x, y, z$ and $w$.

Solution:

As the given matrices are equal, therefore, their corresponding elements must be equal. Comparing the corresponding elements, we get

$x y=8 \quad 4=w$

$z+6=0 \quad x+y=6$

On simplifying, we get

$x=2, y=4, z=-6, w=4 \quad$ or $\quad x=4, y=2, z=-6, w=4$

Hence, the values of $x, y, z$ and $w$ is $2,4,-6,4$ or $4,2,-6,4$.