Itema

Does the following linear system have exactly one solution, infinitely many solutions, or no solutions?

\begin{equation*} \begin{alignedat}{4} x \amp {}+{} \amp y \amp {}+{} \amp 2z \amp {}={} \amp 1 \\ 2x \amp {}-{} \amp y \amp {}-{} \amp 2z \amp {}={} \amp 2 \\ -x \amp {}+{} \amp y \amp {}+{} \amp z \amp {}={} \amp 0 \\ \end{alignedat} \end{equation*}
in-context