Answer
$\left\{\begin{array}{l}
-x+z=-4\\
-y=2\\
y+z=4
\end{array}\right.$
Work Step by Step
The product on the LHS is between a $3\times\underline{3}$ and a $\underline{3}\times$1 matrix,
resulting in a $3\times 1$ matrix:
$\left[\begin{array}{l}
-1x+0y+1z\\
0x-1y+0z\\
0x+1y+1z
\end{array}\right]=\left[\begin{array}{l}
-x+z\\
-y\\
y+z
\end{array}\right]$
Equating matrices, (equating corresponding elements),
we have the system
$\left\{\begin{array}{l}
-x+z=-4\\
-y=2\\
y+z=4
\end{array}\right.$
