Question Bank NAT • 2 Marks Section 1: Mathematical Physics Mathematical Physics - Module 4

QB_PH_014: Mathematical Physics - Module 4

Question Statement

For the matrix $A = \begin{pmatrix} 2 & 1 \\ 1 & 2 \end{pmatrix}$, by the Cayley-Hamilton theorem, $A^2 - 4A = k I$. The value of $k$ is:
Correct Answer
-3, -3
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: Characteristic polynomial: $\lambda^2 - 4\lambda + 3 = 0 \implies A^2 - 4A = -3I$.
← Prev (QB_PH_013) Next (QB_PH_015) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and official TCS iON calculator.

Launch CBT Mock Test