Chapter 2.4, Problem 19E

In Exercises 19–22, use the fact that the following two matrices are inverses of each other to solve the system of linear equations.

$\left[\begin{array}{ccc}1& 2& 2\\ 1& 3& 2\\ 1& 2& 3\end{array}\right]$ and $\left[\begin{array}{ccc}5& -2& -2\\ -1& 1& 0\\ -1& 0& 1\end{array}\right]$

$\{\begin{array}{c}x+2y+2z=1\\ x+3y+2z=-1\\ x+2y+3z=-1\end{array}$