Chapter 9.RP, Problem 10RP

In Problems 7-10, find a general solution for the system $x^{\prime }\left(t\right)=Ax\left(t\right)+f\left(t\right)$, where $A$ and $f\left(t\right)$ are given.

$A=\left[\begin{array}{ccc}2& -2& 3\\ 0& 3& 2\\ 0& -1& 2\end{array}\right]$, $f\left(t\right)=\left[\begin{array}{c}{e}^{-t}\\ 2\\ 1\end{array}\right]$