Chapter 9.7, Problem 3E

In Problems 1-6, use the method of undetermined coefficient to find the a general solution to the system $x^{\prime }\left(t\right)=Ax\left(t\right)+f\left(t\right)$, where $A$ and $f\left(t\right)$ are given.

$A=\left[\begin{array}{ccc}1& -2& 2\\ -2& 1& 2\\ 2& 2& 1\end{array}\right]$, $f\left(t\right)=\left[\begin{array}{c}2e^t\\ 4e^t\\ -2e^t\end{array}\right]$