###### Item 1.2.5.2.d

This is not in reduced row echelon form since the leading entries appear in the wrong order.

\begin{equation*}
\left[
\begin{array}{rrrr|r}
0 \amp 0 \amp 1 \amp 0 \amp -1 \\
0 \amp 1 \amp 0 \amp 0 \amp 3 \\
1 \amp 1 \amp 1 \amp 1 \amp 2 \\
\end{array}
\right]
\sim
\left[
\begin{array}{rrrr|r}
1 \amp 0 \amp 0 \amp 1 \amp 0 \\
0 \amp 1 \amp 0 \amp 0 \amp 3 \\
0 \amp 0 \amp 1 \amp 0 \amp -1 \\
\end{array}
\right]\text{.}
\end{equation*}

Since \(x_4\) is a free variable, there are infinitely many solutions.