Chapter 6.4, Problem 27E

Let
$A=\left(\begin{array}{cc}0& 1\\ 1& 0\end{array}\right)$
Write A as a sum ${\lambda }_1{u}_1{u}_1^T+{\lambda }_2{u}_2{u}_2^T,$ where ${\lambda }_1$ and ${\lambda }_2$ are eigenvalues and $u_1$ and $u_2$ are orthonormal eigenvectors.