Question Bank • QB_SUB_EM_0201 NAT • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra: Eigenvalues & Cayley-Hamilton

Subtopic: Eigenvalues and eigenvectors

Question Statement:

A $2 \times 2$ matrix $M$ has eigenvalues $\lambda_1 = 3$ and $\lambda_2 = 6$. The trace of matrix $M^2$ is:

Answer Key:

45.0

Step-by-Step Solution & Explanation

If $\lambda_i$ are eigenvalues of $M$, then $\lambda_i^2$ are eigenvalues of $M^2$. Trace of $M^2 = \sum \lambda_i^2 = 3^2 + 6^2 = 9 + 36 = 45$.
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