The set of all values of t R, for which the matrix [ 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 ] is invertible, is:

Matrices and Determinants: JEE Main 2023 Mathematics question

JEE Main 2023 · 29 Jan, Evening shift · Q4539

JEE Main 202329 Jan, Evening shiftMathematicsMediumMatrices and Determinants245× since 2002

The set of all values of

\mathrm{t\in \mathbb{R}}

, for which the matrix

\left[ {\matrix{ {{e^t}} & {{e^{ - t}}(\sin t - 2\cos t)} & {{e^{ - t}}( - 2\sin t - \cos t)} \cr {{e^t}} & {{e^{ - t}}(2\sin t + \cos t)} & {{e^{ - t}}(\sin t - 2\cos t)} \cr {{e^t}} & {{e^{ - t}}\cos t} & {{e^{ - t}}\sin t} \cr } } \right]

is invertible, is :

JEE Main 2023 · 29 Jan, Evening shift · Q4539

JEE Main 202329 Jan, Evening shiftMathematicsMediumMatrices and Determinants245× since 2002

The set of all values of

\mathrm{t\in \mathbb{R}}

, for which the matrix

\left[ {\matrix{ {{e^t}} & {{e^{ - t}}(\sin t - 2\cos t)} & {{e^{ - t}}( - 2\sin t - \cos t)} \cr {{e^t}} & {{e^{ - t}}(2\sin t + \cos t)} & {{e^{ - t}}(\sin t - 2\cos t)} \cr {{e^t}} & {{e^{ - t}}\cos t} & {{e^{ - t}}\sin t} \cr } } \right]

is invertible, is :