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Given that $\boldsymbol{\vec{v}_1} = \left\lbrack \begin{array}{r} 3 \\ 2 \end{array} \right\rbrack$ and $\boldsymbol{\vec{v}_2} = \left\lbrack \begin{array}{r} 2 \\ 1 \end{array} \right\rbrack$ are eigenvectors of the matrix $\left\lbrack \begin{array}{rr} 23 & -42 \\ 14 & -26 \end{array} \right\rbrack$ , determine the corresponding eigenvalues.
$\lambda_1 =$
$\lambda_2 =$
Find the solution to the linear system of differential equations $\displaystyle \left\lbrace \begin{array}{rcl} x^{\,\prime} & = & 23x-42y \\ y^{\,\prime} & = & 14x-26y \end{array} \right.$ satisfying the initial conditions $x(0) = 4$ and $y(0) = 3$ .

$x(t) =$
$y(t) =$

You can earn partial credit on this problem.