The set of all values of t \in \mathbb{R}, for which the matrix \left[\begin{array}{cc}e^t & e^{-t\end{array}( \sin t-2 \cos t) , e^{-t}(-2 \sin t-\cos t) ; e^t , e^{-t}(2 \sin t+\cos t) , e^{-t}( \sin t-2 \cos t) ; e^t , e^{-t} \cos t , e^{-t} \sin t ]} is invertible, is [29-Jan-2023 Shift 2]

\{(2 {\k}+1) \frac{\pi}{2}, {\k} \in \mathbb{Z}\}

\{ {\k} \pi+\frac{\pi}{4}, {\k} \in \mathbb{Z}\}

\{ {\k} \pi, {\k} \in \mathbb{Z}\}

JEE Mains 29-Jan-2023 Shift 2 Solved Paper

Section: Mathematics

Question : 68 of 90

Marks: +1, -0

The set of all values of t∈ℝ, for which the matrix
[

]
is invertible, is

[29-Jan-2023 Shift 2]

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