Let M,Nin M3(C) be such that Trace(M^k)=Trace(N^k),qquad 1le kle3 . Which of the following statements is necessarily true?

(C) The characteristic polynomials of M and N are the same.

Q29Section B (Part B)29 of 120

Matrices — equal traces of powers up to the third

Let $M,N\in M_3(\mathbb{C})$ be such that

$\operatorname{Trace}(M^k)=\operatorname{Trace}(N^k),\qquad 1\le k\le3 .$

Which of the following statements is necessarily true?

Pick an option to check your answer.

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