Question: Let P(x) = a0 + a1x + a2x2 + ... + akxk be a polynomial is x. Show that the eigenvalues of matrix p(A) =

Let P(x) = a0 + a1x + a2x2 + ... + akxk be a polynomial is x. Show that the eigenvalues of matrix p(A) = a0In + a1A + a2A2 + .... + akAk are p(λi), i = 1, 2, ......, n, where λi are the eignevalues of A?

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