Part CCSIR NET December 2023cayley-hamilton-remainder

Cayley hamilton remainder

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

A.a + b > 8.
B.a + b < 7.
C.a + b is divisible by 2.
D.a > b.

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The trap it tests

Execution slip

The idea was right. The computation was not.

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Related counterexample: Same characteristic polynomial ⇒ similar

Cayley hamilton remainder

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