\left[ \begin{array}{c c c}
  -1 & -1 & -1 \\
  -1 & -1 & -1 \\
  1 & 3 & 2
\end{array} \right] \rightarrow \left[ \begin{array}{c c c}
   1 & -1 & 0 \\
   0 & 2 & 1
\end{array} \right] \rightarrow x = y \wedge z = -2y