The matrix $$\mathrm{A}=\left[\begin{array}{ccc} -2 &-2 &-1\cr -2 &-2 &1\cr 2 &-2 &-5 \end{array}\right]$$ has eigenvalue $\lambda = -4$ with an eigenspace of dimension 2.
Find a basis for the $-4$-eigenspace:

$\Biggl\lbrace$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

,

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

$\Biggr\rbrace$

(The eigenvalues of $\mathrm{A}$ are $\lambda=-4, -4, -1$.)