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GATE DA 2026 Set 1 — Question 46

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MCQ+2 / -0.67EasyEigenvalue ComputationEigenvalues & EigenvectorsLinear AlgebraTrace of a MatrixMatrix Algebra

Linear Algebra → Eigenvalues & Eigenvectors → Eigenvalue Computation

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Question

Let γ1,γ2,γ3\gamma_1, \gamma_2, \gamma_3 be the eigenvalues of the matrix [1000cos⁡tsin⁡t0−sin⁡tcos⁡t]\begin{bmatrix} 1 & 0 & 0 \\ 0 & \cos t & \sin t \\ 0 & -\sin t & \cos t \end{bmatrix}, where t∈[−π,π]t \in [-\pi, \pi] is in radians.
Which one of the following options lists all the possible values of tt satisfying γ1+γ2+γ3=1+2\gamma_1 + \gamma_2 + \gamma_3 = 1 + \sqrt{2}?
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