Exercise 1

Consider the system of linear equations $$\begin{alignedat}{4} x & {}+{} & 2y & {}-{} & z & {}={} & 1 \\ 3x & {}+{} & 2y & {}+{} & 2z & {}={} & 7 \\ -x & & & {}+{} & 4z & {}={} & -3 \\ \end{alignedat}$$.

1. Find the matrix $A$ and vector $\bvec$ that expresses this linear system in the form $A\xvec=\bvec$.

2. Give a description of the solution space to the equation $A\xvec = \bvec$.