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MCQMediumJEE Main 2023 · 29 January, Shift 2Determinants Basics

Mathematics Question from JEE Main 2023 · 29 January, Shift 2

The set of all values of t∈Rt \in \mathbb{R}, for which the matrix

[ete−t(sin⁡t−2cos⁡t)e−t(−2sin⁡t−cos⁡t)ete−t(2sin⁡t+cos⁡t)e−t(sin⁡t−2cos⁡t)ete−tcos⁡te−tsin⁡t]\begin{bmatrix} e^t & e^{-t}(\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 \end{bmatrix}

is invertible, is:

  • A

    {(2k+1)π2,k∈Z}\{(2k+1)\frac{\pi}{2}, k \in \mathbb{Z}\}

  • B

    {kπ+π4,k∈Z}\{k\pi + \frac{\pi}{4}, k \in \mathbb{Z}\}

  • C

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

  • D

    R\mathbb{R}

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