Allied & ICAR Exam Bank • ALLIED_2621 NAT • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

A $2 \times 2$ matrix $A$ has trace equal to $7$ and determinant equal to $10$. The absolute difference between its two eigenvalues $|\lambda_1 - \lambda_2|$ is:

Answer Key:

3

Step-by-Step Solution & Explanation

Characteristic equation: $\lambda^2 - 7\lambda + 10 = 0 \implies (\lambda - 2)(\lambda - 5) = 0$. Eigenvalues are $2$ and $5$. $|5 - 2| = 3$.
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