GATE AG 2021 • Q50 NAT • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

Summation of eigenvalues of a matrix $\begin{bmatrix} 4 & 1 \\ 3 & 6 \end{bmatrix}$ is ______. [round off to the nearest integer]

Official Answer Key:

10 to 10

Step-by-Step Solution & Explanation

Sum of eigenvalues of a matrix always equals its trace: λ₁+λ₂ = 4+6 = 10 (independent of the off-diagonal entries). Section 2 — Farm Machinery

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