Find the eigenvalues $\lambda_1 < \lambda_2 < \lambda_3$ and corresponding eigenvectors of the matrix $$A = \left[\begin{array}{ccc} -5 &-6 &54\cr 0 &1 &10\cr 0 &0 &3 \end{array}\right].$$
The eigenvalue $\lambda_1 =$ corresponds to the eigenvector $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$.

The eigenvalue $\lambda_2 =$ corresponds to the eigenvector $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$.

The eigenvalue $\lambda_3 =$ corresponds to the eigenvector $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$.