Problem 1. Let A E Mn(F) be diagonalizable, and let p(t) = artk +..+ ast + ao be a polynomial such that p(A) akAk + ...+ a, A+ aoI = 0. = 0 for all eigenvalues A of A. Show that p(A) %3!

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Problem 1. Let A E Mn(F) be diagonalizable, and let p(t) = artk + ...+ art + ao
be a polynomial such that p() = 0 for all eigenvalues A of A. Show that p(A)
ak Ak + ...+ a, A+ aoI = 0.
Transcribed Image Text:Problem 1. Let A E Mn(F) be diagonalizable, and let p(t) = artk + ...+ art + ao be a polynomial such that p() = 0 for all eigenvalues A of A. Show that p(A) ak Ak + ...+ a, A+ aoI = 0.
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