Allied & ICAR Exam Bank • ALLIED_0006 NAT • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

The maximum eigenvalue of the matrix $A = \begin{pmatrix} 4 & 2 \\ 2 & 1 \end{pmatrix}$ is:

Answer Key:

5

Step-by-Step Solution & Explanation

Characteristic polynomial: $(4 - \lambda)(1 - \lambda) - 4 = \lambda^2 - 5\lambda = 0 \implies \lambda = 0, 5$. Maximum eigenvalue is $5$.
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