Iteme

This is not in reduced row echelon form because the leading entry in the second and third rows are not the only nonzero elements in their columns. We can use replacement operations to remedy this.

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

This system has the single solution \((-1,2,1)\text{.}\)

in-context