Chapter 7.2, Problem 10E

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

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

(See Exercise 22, 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.

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