Find the singular values $\sigma_1 \ge \sigma_2$ of $$A = \left[\begin{array}{cc} -2 &-1\cr -1 &-2 \end{array}\right].$$
$\sigma_1 =$ ,
$\sigma_2 =$ .

Find unit vectors $\vec{v}_1$ and $\vec{v}_2$ such that $\| A\vec{v}_1 \| = \sigma_1$ and $\| A\vec{v}_2 \| = \sigma_2$.

$\vec{v}_1=$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$

$\vec{v}_2=$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$