Answer
$\left\{\begin{array}{rrrrr}
x & -y & +4z & =-3\\
-\frac{1}{3}x & -3y & +\frac{1}{3}z & =-1\\
3x & & +z & =0
\end{array}\right.$
Work Step by Step
The product of the two matrices on the LHS is a 3$\times$1 matrix:
$\left[\begin{array}{l}
x-y+4z\\
-\frac{1}{3}x-3y+\frac{1}{3}z\\
3x+0+z
\end{array}\right].\qquad $Equating it to $\left[\begin{array}{l}
-3\\
-1\\
2
\end{array}\right]$ leads to
the system of equations
$\left\{\begin{array}{llll}
x & -y & +4z & =-3\\
-\frac{1}{3}x & -3y & +\frac{1}{3}z & =-1\\
3x & & +z & =0
\end{array}\right.$
