JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The set of all values of \(t \in R\), for which the matrix \(\left[\begin{array}{ccc}e^t & e^{-t}(\sin t-2 \cos t) & e^{-t}(-2 \sin t-\cos t) \\e^t & e^{-t}(2 \sin t+\cos t) & e^{-t}(\sin t-2 \cos t) \\e^t & e^{-t} \cos t & e^{-t} \sin t \end{array}\right]\) is invertible.
- A \(\left\{(2 k +1) \frac{\pi}{2}, k \in Z \right\}\)
- B \(\left\{ k \pi+\frac{\pi}{4}, k \in Z \right\}\)
- C \(\{ k \pi, k \in Z \}\)
- D \(R\)
Answer & Solution
Correct Answer
(D) \(R\)
Step-by-step Solution
Detailed explanation
If its invertible, then determinant value \(\neq 0\) So, \(\left|\begin{array}{ccc}e^t & e^{-t}(\sin t-2 \cos t) & e^{-t}(-2 \sin t-\cos t) \\ e^t & e^{-t}(2 \sin t+\cos t) & e^{-t}(\sin t-2 \cos t) \\ e^t & e^{-t} \cos t & e^{-t} \sin t\end{array}\right| \neq 0\)…
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