Item1.2.5.2.a

This is not in reduced row echelon form since the leading entry in the second row is not the only nonzero entry in its column. Applying a replacement operation gives,

\begin{equation*} \left[ \begin{array}{rrrr|r} 1 \amp 1 \amp 0 \amp 3 \amp 3 \\ 0 \amp 1 \amp 0 \amp -2 \amp 1 \\ 0 \amp 0 \amp 1 \amp 3 \amp 4 \\ \end{array} \right] \sim \left[ \begin{array}{rrrr|r} 1 \amp 0 \amp 0 \amp 5 \amp 2 \\ 0 \amp 1 \amp 0 \amp -2 \amp 1 \\ 0 \amp 0 \amp 1 \amp 3 \amp 4 \\ \end{array} \right]\text{.} \end{equation*}

There are infinitely many solutions since \(x_4\) is a free variable.

in-context