Chapter 7.1, Problem 4E

Verifying Eigenvalues and Eigenvectors in Exercises 1-6, verify that ${\lambda }_i$ is an eigenvalues of A and that $X_i$ is a corresponding eigenvector.

$\text{A}=\left[\begin{array}{ccc}-2& 2& -3\\ 2& 1& -6\\ -1& -2& 0\end{array}\right]$, $\begin{array}{l}{\lambda }_1=5,X_1=\left(1,\text{ 2, }-1\right)\\ {\lambda }_2=-3,X_2=\left(-2,1\text{, 0}\right)\\ {\lambda }_3=-3,X_3=\left(3,0\text{, 1}\right)\end{array}$