in ${ℝ}^3$

$ℒ=\left(\begin{array}{ccc}-7& 6& 4\\ -3& 2& 2\\ -3& 3& 1\end{array}\right)\begin{array}{ccc}p\left(x\right)& =& det(x{ℐ}_3-ℒ)\\ & =& 2+5x+4x^2+x^3\\ & =& (x+2){(x+1)}^2\end{array}$

Eigenvalue ${\lambda }_1=-2$

$\left(\begin{array}{cccc}5& -6& -4& 0\\ 3& -4& -2& 0\\ 3& -3& -3& 0\end{array}\right)\stackrel{}{\to }\left(\begin{array}{cccc}1& 0& -2& 0\\ 0& 1& -1& 0\\ 0& 0& 0& 0\end{array}\right)$

Eigenvalue ${\lambda }_2=-1$

$\left(\begin{array}{cccc}6& -6& -4& 0\\ 3& -3& -2& 0\\ 3& -3& -2& 0\end{array}\right)\stackrel{}{\to }\left(\begin{array}{cccc}3& -3& -2& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right)$