GATE AG 2017 • Q3 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

Characteristic equation of the matrix $\begin{bmatrix} 2 & \sqrt{2} \\ \sqrt{2} & 1 \end{bmatrix}$ with eigenvalue $\lambda$ is

Options:

  • (A) $\lambda^2 + 3\lambda + 4 = 0$
  • (B) $\lambda^2 + 3\lambda - 2 = 0$
  • (C) $\lambda^2 - 3\lambda = 0$
  • (D) $\lambda^2 + 3\lambda = 0$

Official Answer Key:

C

Step-by-Step Solution & Explanation

• For a 2×2 matrix, the characteristic equation is λ² – (trace)λ + det(A) = 0. • Trace = 2 + 1 = 3. • det(A) = (2)(1) – (√2)(√2) = 2 – 2 = 0. • Characteristic equation: λ² – 3λ + 0 = 0, i.e. λ² – 3λ = 0. • Distractor logic: (A) and (B) use an incorrect determinant (treating √2×√2 as something other than 2, or adding instead of subtracting); (D) flips the sign of the trace term. • Final Answer: (C) λ² – 3λ = 0

Practice This in Real CBT Exam Interface

Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.

Launch CBT Mock Test