##### Exercise1

Consider the matrix

\begin{equation*} A = \left[\begin{array}{rrrr} 3 \amp -1 \amp 1 \amp 4 \\ 0 \amp 2 \amp 3 \amp 1 \\ -2 \amp 1 \amp 0 \amp -2 \\ 3 \amp 0 \amp 1 \amp 2 \\ \end{array}\right] \text{.} \end{equation*}

1. Explain why $$A$$ has an inverse.

2. Find the inverse of $$A$$ by augmenting by the identity $$I$$ to form $$\left[\begin{array}{r|r}A \amp I \end{array}\right]\text{.}$$

3. Use your inverse to solve the equation $$A\xvec = \fourvec{3}{2}{-3}{-1}\text{.}$$

in-context