in ${ℝ}^3$

$ℒ=\left(\begin{array}{ccc}12& -18& -8\\ 5& -8& -3\\ 11& -15& -8\end{array}\right)\begin{array}{ccc}p\left(x\right)& =& det(x{ℐ}_3-ℒ)\\ & =& 2+5x+4x^2+x^3\\ & =& (x+2){(x+1)}^2\end{array}$

Eigenvalue ${\lambda }_1=-2$

$\left(\begin{array}{cccc}-14& 18& 8& 0\\ -5& 6& 3& 0\\ -11& 15& 6& 0\end{array}\right)\stackrel{}{\to }\left(\begin{array}{cccc}1& 0& -1& 0\\ 0& 3& -1& 0\\ 0& 0& 0& 0\end{array}\right)$

Eigenvalue ${\lambda }_2=-1$

$\left(\begin{array}{cccc}-13& 18& 8& 0\\ -5& 7& 3& 0\\ -11& 15& 7& 0\end{array}\right)\stackrel{}{\to }\left(\begin{array}{cccc}1& 0& -2& 0\\ 0& 1& -1& 0\\ 0& 0& 0& 0\end{array}\right)$