##### Itema

Here are the three augmented matrices in reduced row echelon form that we considered in the previous section.

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

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

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

For each matrix, identify the pivot positions and state whether the corresponding system of linear equations is consistent. If the system is consistent, explain whether the solution is unique or whether there are infinitely many solutions.

in-context