jee-main 2019 Q77

jee-main · India · session1_09jan_shift2 Matrices Determinant and Rank Computation

If $A = \left[\begin{array}{ccc} e^t & e^{-t}\cos t & e^{-t}\sin t \\ e^t & -e^{-t}\cos t - e^{-t}\sin t & -e^{-t}\sin t + e^{-t}\cos t \\ e^t & 2e^{-t}\sin t & -2e^{-t}\cos t \end{array}\right]$, then $A$ is:
(1) Invertible only if $t = \pi$
(2) Not invertible for any $t \in R$
(3) Invertible only if $t = \frac{\pi}{2}$
(4) Invertible for all $t \in R$

If $A = \left[\begin{array}{ccc} e^t & e^{-t}\cos t & e^{-t}\sin t \\ e^t & -e^{-t}\cos t - e^{-t}\sin t & -e^{-t}\sin t + e^{-t}\cos t \\ e^t & 2e^{-t}\sin t & -2e^{-t}\cos t \end{array}\right]$, then $A$ is:\\
(1) Invertible only if $t = \pi$\\
(2) Not invertible for any $t \in R$\\
(3) Invertible only if $t = \frac{\pi}{2}$\\
(4) Invertible for all $t \in R$

Paper Questions

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