Itemd

This is not in reduced row echelon form because the row of zeroes should be at the bottom of the matrix. We also need another interchange so that the leading entry in the second row is to the right of the leading entry in the first row.

\begin{equation*} \left[ \begin{array}{rrr|r} 0 \amp 1 \amp 3 \amp 2 \\ 0 \amp 0 \amp 0 \amp 0 \\ 1 \amp 0 \amp 4 \amp 2 \\ \end{array} \right] \sim \left[ \begin{array}{rrr|r} 1 \amp 0 \amp 4 \amp 2 \\ 0 \amp 1 \amp 3 \amp 2 \\ 0 \amp 0 \amp 0 \amp 0 \\ \end{array} \right]. \end{equation*}

Once again, there are infinitely many solutions.

in-context