Allied & ICAR Exam Bank • ALLIED_2615 NAT • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Cayley–Hamilton theorem

Question Statement:

Let $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$. The characteristic equation of $A$ is $\lambda^2 - 5\lambda - 2 = 0$. Using Cayley–Hamilton, $A^2 - 5A = k I$. The value of $k$ is:

Answer Key:

2

Step-by-Step Solution & Explanation

By Cayley–Hamilton, $A^2 - 5A - 2I = 0 \implies A^2 - 5A = 2I$. Hence $k = 2$.
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