Find the eigenvalues and eigenvectors of the matrix $\displaystyle \mathrm{A} = \left\lbrack \begin{array}{rrr} 0 & 4 & 0 \\ 4 & 1 & 2 \\ 0 & 2 & 0 \end{array} \right\rbrack$

$\lambda_1 =$

, $\boldsymbol{\vec{v}_1} =$

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

    and

$\lambda_2 =$

, $\boldsymbol{\vec{v}_2} =$

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

    and

$\lambda_3 =$

, $\boldsymbol{\vec{v}_3} =$

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