For $e^{At} = 1/2\begin{bmatrix}e^{2t}+e^{-t} & e^{2t} - e^{-t} \\ e^{2t}-e^{-t} & e^{2t}+e^{-t}\end{bmatrix}$ for all t $\in$ $\mathbb{R}$. how to find A?
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If you let $\vec{x} = e^{At}$, the $\vec{x}$ would satisfy the ODE $\dfrac{d\vec{x}}{dt} = A \vec{x}$.
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