Find the eigenvalues and eigenvectors of the matrix $\left[\begin{array}{ccc} 9 &-3 &6\cr 0 &2 &0\cr -3 &0 &0 \end{array}\right]$.

$\lambda_1 =$,   $\mathbf{v}_1 =$$\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$

$\lambda_2 =$,   $\mathbf{v}_2 =$$\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$

$\lambda_3 =$,   $\mathbf{v}_3 =$$\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$