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Calculate ${e}^{\mathrm{At}}$ for a Constant Matrix $A$

 Description For a constant matrix $A$, calculate the exponential of the matrix $\mathrm{At}$.

Calculate  for Constant Matrix $\mathbit{A}$

Enter the matrix $A$

Use the Matrix command, the Matrix palette, or an existing matrix

 > $\left[\begin{array}{rr}{4}& {1}\\ {2}& {3}\end{array}\right]$
 $\left[\begin{array}{rr}{4}& {1}\\ {2}& {3}\end{array}\right]$ (1)

Calculate

 > $\mathrm{LinearAlgebra}\left[\mathrm{MatrixExponential}\right]\left(,t\right)$
 $\left[\begin{array}{cc}\frac{{1}}{{3}}{}{{ⅇ}}^{{2}{}{t}}{+}\frac{{2}}{{3}}{}{{ⅇ}}^{{5}{}{t}}& \frac{{1}}{{3}}{}{{ⅇ}}^{{5}{}{t}}{-}\frac{{1}}{{3}}{}{{ⅇ}}^{{2}{}{t}}\\ \frac{{2}}{{3}}{}{{ⅇ}}^{{5}{}{t}}{-}\frac{{2}}{{3}}{}{{ⅇ}}^{{2}{}{t}}& \frac{{2}}{{3}}{}{{ⅇ}}^{{2}{}{t}}{+}\frac{{1}}{{3}}{}{{ⅇ}}^{{5}{}{t}}\end{array}\right]$ (2)

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