Question Bank • QB_SUB_EM_0019 NAT • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

A $2 \times 2$ matrix $M$ has eigenvalues $\lambda_1 = 1$ and $\lambda_2 = 4$. The trace of matrix $M^2$ is:

Answer Key:

17.0

Step-by-Step Solution & Explanation

If $\lambda_i$ are eigenvalues of $M$, then $\lambda_i^2$ are eigenvalues of $M^2$. Trace of $M^2 = \sum \lambda_i^2 = 1^2 + 4^2 = 1 + 16 = 17$.
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