Chapter 9.7, Problem 8E

In Problems 7-10, use the method of undetermined coefficient to determine only the form of a particular 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.

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