Chapter 7.1, Problem 3E

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

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