GATE AG 2008 • Q2 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

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

Options:

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

Official Answer Key:

C

Step-by-Step Solution & Explanation

Characteristic equation: λ² − (trace)λ + det = 0 → λ² − 5λ + (6−2) = λ² − 5λ + 4 = 0 → (λ−1)(λ−4) = 0 → λ = 1, 4.

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