Chapter 6.1, Problem 3P

Verify that $\text{ψ}=\left(\begin{array}{ccc}{e}^t& e^{-2t}& e^{3t}\\ -4e^t& -e^{-2t}& 2e^{3t}\\ -e^t& -e^{-2t}& e^{3t}\end{array}\right)$ satisfies matrix differential equation $\text{ψ'}=\left(\begin{array}{ccc}1& -1& 4\\ 3& 2& -1\\ 2& 1& -1\end{array}\right)\text{ψ}$.