###### Item a

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.