###### Item 1.2.5.2.b

This is not in reduced row echelon form since the leading entries are not all \(1\text{.}\) We can scale those rows to find the reduced row echelon form.

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

There are no solutions since the last row gives the equation \(0=1\text{.}\)