Let γ1, γ2, γ3 be the eigenvalues of the matrix \(\begin{bmatrix}1&0&0\\0&\cos…

GATE · 2026 · DA · Data Science & AI

Let γ1, γ2, γ3 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] is in radians. Which one of the following options lists all the possible values of t satisfying γ1+γ2+γ3=1+2\gamma_1+\gamma_2+\gamma_3=1+\sqrt{2}?

  1. A.

    {π/3, −π/4}

  2. B.

    {π/4, −π/3}

  3. C.

    {π/4, −π/4}

  4. D.

    {π/3, −π/3}

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