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Matrices and Determinants question

2019 · 9 Jan · Shift 2 · Q33
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  5. /2019 · 9 Jan · Shift 2 · Q33

Matrices and Determinants question

2019 · 9 Jan · Shift 2 · Q33

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1
If A=[ete−tcos⁡te−tsin⁡tet−e−tcos⁡t−e−tsin⁡t−e−tsin⁡t+e−tcosolimitstet2e−tsin⁡t−2e−tcos⁡t]A = \left[ {\begin{matrix} {{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}}co{\mathop{\rm s} olimits} t} \\ {{e^t}} & {2{e^{ - t}}\sin t} & { - 2{e^{ - t}}\cos t} \\ \end{matrix} } \right]A=​etetet​e−tcost−e−tcost−e−tsint2e−tsint​e−tsint−e−tsint+e−tcosolimitst−2e−tcost​​ then A is :
  1. A
    invertible for all t ∈\in∈ R.
  2. B
    invertible only if t =π=\pi=π
  3. C
    not invertible for any t ∈\in∈ R
  4. D
    invertible only if t =π2={\pi \over 2}=2π​.
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