e^{tA} = \left[ {\begin{array}{*{20}c}
 {e^t } & {2te^t } & { - 7e^t + 7e^{2t} - 4te^t } \\
 0 & {e^t } & { - 2e^t + 2e^{2t} } \\
 0 & 0 & {e^{2t} } \\

 \end{array} } \right]