\left[\begin{array}{ccc|c}
1 & \lambda & 1 & -2 \\
-\lambda & -4 & 2 & \mu \\
2 & 3 & 3 & 0
\end{array}\right] & \sim
\left[\begin{array}{ccc|c}
1 & \lambda & 1 & -2 \\
-\lambda - 2 & -4 - 2 \lambda & 0 & \mu + 4 \\
-1 & 3 - 3 \lambda & 0 & 6
\end{array}\right] \sim
\left[\begin{array}{ccc|c}
0 & 3 - 2 \lambda & 1 & 4 \\
0 & (\lambda + 2)(3 \lambda - 5) & 0 & \mu - 6 \lambda - 2 \\
-1 & 3 - 3 \lambda & 0 & 6
\end{array}\right]