The matrix $\displaystyle \mathrm{A} = \left\lbrack \begin{array}{rrr} 1 & -1 & 0 \\ -2 & -3 & -6 \\ 2 & 3 & 7 \end{array} \right\rbrack$ has an eigenvalue $\displaystyle \lambda = -1.$
Find an eigenvector for this eigenvalue.

$\boldsymbol{\vec{v}} =$

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

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Note: You should solve the following problem WITHOUT computing all eigenvalues.

The matrix $\displaystyle \mathrm{B} = \left\lbrack \begin{array}{rrr} 0 & -2 & -8 \\ 5 & -1 & 4 \\ -1 & 2 & 4 \end{array} \right\rbrack$ has an eigenvector $\displaystyle \boldsymbol{\vec{v}} = \left\lbrack \begin{array}{r} -2 \\ -2 \\ 1 \end{array} \right\rbrack.$
Find the eigenvalue for this eigenvector.

$\lambda =$