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Part CCSIR NET December 2023cayley-hamilton-remainder

Cayley hamilton remainder

Consider A = [[1, 4], [2, 3]]. Suppose A5−4A4−7A3+11A2−A−10I=A^{5} - 4A^{4} - 7A^{3} + 11A^{2} - A - 10I = aA + bI for some a,b∈Za, b \in \mathbb{Z}. Which of the following statements are true?

  1. A.a + b > 8.
  2. B.a + b < 7.✓ Correct
  3. C.a + b is divisible by 2.✓ Correct
  4. D.a > b.

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Related counterexample: Same characteristic polynomial ⇒ similar

More on this topic

The chapter behind this: Characteristic vs minimal polynomial — what each tells you — free to read

From Eigenvalues and Canonical Forms › Eigenvalues, characteristic & minimal polynomials, Cayley–Hamilton

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