Exercise 2.1.19

$E=\left[\begin{array}{ccc}1\hfill & 0\hfill & 0\hfill \\ 0\hfill & 1\hfill & 0\hfill \\ 1\hfill & 0\hfill & 1\hfill \end{array}\right]$and $E^{-1}=\left[\begin{array}{ccc}\hfill 1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill \\ \hfill -1\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right],Ev=\left[\begin{array}{c}\hfill 3\hfill \\ \hfill 4\hfill \\ \hfill 8\hfill \end{array}\right]$and $E^{-1}Ev$ recovers $\left[\begin{array}{c}3\hfill \\ 4\hfill \\ 5\hfill \end{array}\right]$