Exercise1

Consider the system of linear equations

\begin{equation*} \begin{alignedat}{4} x \amp {}+{} \amp 2y \amp {}-{} \amp z \amp {}={} \amp 1 \\ 3x \amp {}+{} \amp 2y \amp {}+{} \amp 2z \amp {}={} \amp 7 \\ -x \amp \amp \amp {}+{} \amp 4z \amp {}={} \amp -3 \\ \end{alignedat} \text{.} \end{equation*}
  1. Find the matrix \(A\) and vector \(\bvec\) that expresses this linear system in the form \(A\xvec=\bvec\text{.}\)

  2. Give a description of the solution space to the equation \(A\xvec = \bvec\text{.}\)

in-context