Given:

$\frac{dx}{dt}=65x+42y$

$\frac{dy}{dt}=-99x-64y$

Verify $v_1=\left[\begin{array}{c}2\\ -3\end{array}\right]$ and $v_2=\left[\begin{array}{c}-7\\ 11\end{array}\right]$ are the eigenvectors of the coefficient matrix of

the above equations. Find associated eigenvalues.

Find the solution for the equations provided above when

$x(0)=\left[\begin{array}{c}-14\\ 22\end{array}\right]$