Allied & ICAR Exam Bank • ALLIED_0020 NAT • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Cayley–Hamilton theorem

Question Statement:

If $A = \begin{pmatrix} 1 & 2 \\ 0 & 2 \end{pmatrix}$, the trace of $A^2$ is:

Answer Key:

5

Step-by-Step Solution & Explanation

Eigenvalues of $A$ are $1$ and $2$. The eigenvalues of $A^2$ are $1^2 = 1$ and $2^2 = 4$. Trace $= 1 + 4 = 5$.
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