# 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.
$$\displaystyleλ{1}=-{1}\to{\left\lbrace\begin{array}{cc} {1}&{1}\end{array}\right\rbrace},λ{2}={2}\to{\left\lbrace\begin{array}{cc} {1}&-{1}\end{array}\right\rbrace}$$

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Aniqa O'Neill
$$\displaystyle{y}{1}={c}{1}{e}^{{-{{t}}}}+{c}{2}{e}^{{2}}{t}$$
$$\displaystyle{y}{2}={c}{1}{e}^{{-{{t}}}}-{c}{2}{e}^{{2}}{t}$$