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For the linear system

$\displaystyle \boldsymbol{ \vec{y}^{\,\prime} } = \left\lbrack \begin{array}{rr} 4 & 2 \\ -1 & 1 \end{array} \right\rbrack \boldsymbol{\vec{y}}$
Find the eigenvalues and eigenvectors for the coefficient matrix.

$\lambda_1 =$

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

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

, and $\lambda_2 =$

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

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