Answer
$x=-2, $ $y=3,$ and $z=1$
Work Step by Step
Operating on the corresponding elements, the given matrix equation, $ \begin{bmatrix}
2 & 2
\\
-1 & 6
\end{bmatrix}
-
\begin{bmatrix}
4 & -1
\\
0 & 5
\end{bmatrix}
=
\begin{bmatrix}
x & y
\\
-1 & z
\end{bmatrix}
,$ implies the following equations:
\begin{align*}
\begin{array}{cccc}
2-4=x &&2-(-1)=y && 6-5=z
\end{array}
.\end{align*}
Simplifying the equations above results to
\begin{align*}
\begin{array}{cccc}
-2=x &&2+1=y && 1=z
\\
&&3=y
\end{array}
.\end{align*}
Hence, $
x=-2, $ $y=3,$ and $z=1
$.
