Chapter 7.1, Problem 1E

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

$\text{A}=\left[\begin{array}{cc}2& 0\\ 0& -2\end{array}\right]$, $\begin{array}{l}{\lambda }_1=2,{\text{x}}_1=\left(1,\text{ 0}\right)\\ {\lambda }_2=-2,{\text{x}}_2=\left(0,\text{ 1}\right)\end{array}$