Question: 16. (a) Let T be a linear operator on a vector space V, and let x be an eigenvector of T corresponding to the

16. (a) Let T be a linear operator on a vector space V, and let x be an eigenvector of T corresponding to the eigenvalue A. For any positive integer m. prove that x is an eigenvector of 7" corresponding to the eigenvalue ". (b) State and prove the analogous result for matrices.

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