Given [A = [ *20c 10 01 ]] the state transition matrix eAt is given by

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Control Systems

Given \[A = \left[ {\begin{array}{*{20}{c}} 1&0\\ 0&1 \end{array}} \right]\] the state transition matrix e^At is given by

A) \[\left[ {\begin{array}{*{20}{c}} 0&{{e^{ - t}}}\\ {{e^{ - t}}}&0 \end{array}} \right]\] B) \[\left[ {\begin{array}{*{20}{c}} {{e^t}}&0\\ 0&{{e^t}} \end{array}} \right]\] C) \[\left[ {\begin{array}{*{20}{c}} {{e^{ - t}}}&0\\ 0&{{e^{ - t}}} \end{array}} \right]\] D) \[\left[ {\begin{array}{*{20}{c}} 0&{{e^t}}\\ {{e^t}}&0 \end{array}} \right]\]

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Correct Answer: Option B

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Given A = left begin array 20 c 1&0 0&1 end...

Given \[A = \left[ {\begin{array}{*{20}{c}} 1&0\\ 0&1 \end{array}} \right]\] the state transition matrix eAt is given by

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Given \[A = \left[ {\begin{array}{*{20}{c}} 1&0\\ 0&1 \end{array}} \right]\] the state transition matrix e^At is given by