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Linear Algebra
Paper I, Q5(a) • CSE 2023
14/20
Approach5/6
Execution5/8
Rigor4/6
Approach & Method
5/6- Correct use of Cayley-Hamilton theorem as the primary approach.
- Efficient method selection — this is the most direct path to the solution.
- Consider stating the theorem formally before applying it. UPSC examiners award 1-2 marks for explicit theorem statements.
Step 3: Matrix multiplication error
You wrote: A² = [4, 2; 1, 3]Correct: A² = [4, 2; 2, 3]
The (2,1) entry should be (1×1 + 1×1) = 2, not 1.
Examiner's Tip
"For eigenvalue problems, UPSC examiners prefer the characteristic equation method over direct computation. It shows deeper understanding and earns full marks even if you make a minor arithmetic error later."
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