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