GATE AG 2026 • Q37 MCQ • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

The determinant of a 2 × 2 square matrix is 1.6. If the sum of the eigen values is −2.8, the eigen values are

Options:

  • (A) −2 and −0.8
  • (B) −1.8 and −1
  • (C) −3 and 0.2
  • (D) −1.2 and −1.6

Official Answer Key:

A

Step-by-Step Solution & Explanation

Two standard properties: Sum of eigen values = trace = −2.8 Product of eigen values = determinant = 1.6 Characteristic equation: λ² − (sum)λ + (product) = 0 λ² + 2.8λ + 1.6 = 0 λ = [−2.8 ± √(7.84 − 6.4)]/2 = (−2.8 ± √1.44)/2 = (−2.8 ± 1.2)/2 λ₁ = −0.8, λ₂ = −2.0 Check: (−2)(−0.8) = 1.6 ✔ ; (−2) + (−0.8) = −2.8 ✔

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