Find the state transition matrix \({\rm{\Phi }}\left( t \right)\;if\;A = \left[ {\begin{array}{*{20}{c}} 0&{ - 2}\\ 1&{ - 3} \end{array}} \right]\)
1
\(\left[ {\begin{array}{*{20}{c}} {\left( {2{e^{ - t}} - {e^{ - 2t}}} \right)}&{\left( {{e^{ - t}} - {e^{ - 2t}}} \right)}\\ {\left( { - 2{e^{ - t}} + 2{e^{ - 2t}}} \right)}&{\left( { - {e^{ - t}} + 2{e^{ - 2t}}} \right)} \end{array}} \right]\)
2
\(\left[ {\begin{array}{*{20}{c}} {\left( {2{e^{ - t}} - {e^{ - 2t}}} \right)}&{\left( { - 2{e^{ - t}} + 2{e^{ - 2t}}} \right)}\\ {\left( {{e^{ - t}} + {e^{ - 2t}}} \right)}&{\left( { - {e^{ - t}} + 2{e^{ - 2t}}} \right)} \end{array}} \right]\)
3
\(\left[ {\begin{array}{*{20}{c}} {\left( {2{e^{ - t}} - {e^{ - 2t}}} \right)}&{\left( { - 2{e^{ - t}} + 2{e^{ - 2t}}} \right)}\\ {\left( {{e^{ - t}} - {e^{ - 2t}}} \right)}&{\left( { - {e^{ - t}} + 2{e^{ - 2t}}} \right)} \end{array}} \right]\)
4
\(\left[ {\begin{array}{*{20}{c}} {\left( {2{e^{ - t}} + {e^{ - 2t}}} \right)}&{\left( { - 2{e^{ - t}} + 2{e^{ - 2t}}} \right)}\\ {\left( {{e^{ - t}} - {e^{ - 2t}}} \right)}&{\left( { - {e^{ - t}} + 2{e^{ - 2t}}} \right)} \end{array}} \right]\)