GATE AG 2014 • Q36 MCQ • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

The eigenvalues of the matrix $A = \begin{bmatrix} 2 & 2 \\ -1 & 5 \end{bmatrix}$ are

Options:

  • (A) 1 and 2
  • (B) 2 and 3
  • (C) 3 and 4
  • (D) 4 and 5

Official Answer Key:

C

Step-by-Step Solution & Explanation

Characteristic equation: det(A − λI) = 0 (2−λ)(5−λ) − (2)(−1) = 0 10 − 2λ − 5λ + λ² + 2 = 0 λ² − 7λ + 12 = 0 ⇒ (λ−3)(λ−4) = 0 λ = 3 and 4. Answer: (C).

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