Question: 3.17. Let A be a square matrix with an eigenvalue c and corresponding eigen- vector v. Consider the matrix polynomial in A p( A) =

3.17. Let A be a square matrix with an eigenvalue c and corresponding eigen- vector v. Consider the matrix polynomial in A p( A) = bol+bjA + ...+ bRAk. Show that if (c, v) is an eigenpair of A, then p(c), that is, bot bict ... + back, is an eigenvalue of p(A) with corresponding eigenvector v. (Technically, the symbol p(.) is overloaded in these two instances.)

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