Chapter 7.2, Problem 9E

Diagonalizing a Matrix In Exercise 7-14, find (if possible) a nonsingular matrix P such that $P^{-1}AP$is diagonal. Verify that $P^{-1}AP$is a diagonal matrix with the eigenvalues on the main diagonal

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

(See Exercise 20, section 7.1.)

Characteristic Equation, Eigenvalues, and Eigenvectors in Exercise 15-28, find (a) the characteristics equation and (b) the eigenvalues (and corresponding eigenvectors) of the matrix.

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