GATE AG 2013 • Q4 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

Eigenvalues of the matrix $\begin{bmatrix} 2 & 1 \\ 3 & 2 \end{bmatrix}$ are

Options:

  • (A) $2i$
  • (B) $2 \pm 3i$
  • (C) $2 \pm \sqrt{3}i$
  • (D) $2 \pm \sqrt{3}$

Official Answer Key:

D

Step-by-Step Solution & Explanation

Characteristic equation: det(A−λI) = (2−λ)² − 3 = 0 ⇒ (2−λ)² = 3 ⇒ 2−λ = ±√3 ⇒ λ = 2∓√3, i.e., λ = 2±√3 (real, since discriminant of λ²−4λ+1=0 is 16−4=12>0). Answer: (D). (Verified symbolically.)

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