Item1.2.5.2.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.

in-context