The coefficient matrix for a system of linear differential equations of the form y′=Ay has the given eigenvalues and eigenspace bases.

The coefficient matrix for a system of linear differential equations of the form y′=Ay has the given eigenvalues and eigenspace bases. Find the general solution for the system.
$\lambda 1=-1\to \left\{\begin{array}{cc}1& 1\end{array}\right\},\lambda 2=2\to \left\{\begin{array}{cc}1& -1\end{array}\right\}$
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Aniqa O'Neill
$y1=c1{e}^{-t}+c2{e}^{2}t$
$y2=c1{e}^{-t}-c2{e}^{2}t$