##### Itema

Write the augmented matrix for the system of equations

\begin{equation*} \begin{alignedat}{4} x \amp {}+{} \amp 2y \amp {}-{} \amp z \amp {}={} \amp 1 \\ 3x \amp {}+{} \amp 2y \amp {}+{} \amp 2z \amp {}={} \amp 7 \\ -x \amp \amp \amp {}+{} \amp 4z \amp {}={} \amp -3 \\ \end{alignedat} \end{equation*}and perform Gaussian elimination to describe the solution space of the system of equations in as much detail as you can.