Chapter 5.4, Problem 24P

In each of Problems $20$ through $24$, use a computer algebra system to assist in solving the given initial value problem by the method of Laplace transforms:

$y\text{'}=\left(\begin{array}{ccc}0& 1& -1\\ 1& 0& 1\\ 1& 1& 0\end{array}\right)y+\left(\begin{array}{c}0\\ -e^{-t}\\ e^t\end{array}\right),y\left(0\right)=\left(\begin{array}{c}1\\ 2\\ 3\end{array}\right)$.