###### Item1.2.5.2.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 $$0=1\text{.}$$

in-context