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If $A = \begin{bmatrix} e^t & e^{-1}\cos t & e^{-1}\sin t \ e^t & -e^{-1}\cos t - e^{-1}\sin t & -e^{-1}\sin t + e^{-1}\cos t \ e^t & 2e^{-1}\sin t & -2e^{-1}\cos t \end{bmatrix}$
then $A$ is:
(1) invertible for all $t \in \mathbb{R}$.
(2) invertible only if $t = \pi$.
(3) not invertible for any $t \in \mathbb{R}$.
(4) invertible only if $t = \dfrac{\pi}{2}$
BETA
