Exams › JEE Main › Maths
If A = [[e^t, e^(-t) cos t, e^(-t) sin t], [e^t, -e^(-t) cos t, -e^(-t) sin t], [e^t, 2e^(-t) sin t, -2e^(-t) cos t]] then A is:
- invertible only if t = π
- invertible for all t ∈ R
- invertible only if t = π/2
- not invertible for any t ∈ R
Correct answer: invertible for all t ∈ R
Solution
Computing the determinant gives det(A) = 4e^(-t), which is nonzero for every real t. Hence A is invertible for all t in R.
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