Let f E Pn(C) be a polynomial of degree n. a) Prove that B(f) = (f,...

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Let f E Pn(C) be a polynomial of degree n. a) Prove that B(f) = (f, f', f",..., f(n)) is a basis for Pn(C), where f(k) is the kth derivative of f. b) Let f = (x – 1)*, and find the matrices 8() Ia and aIBf), where a = (1, x, x2, x) is the standard basis for P3 (C). Let f E Pn(C) be a polynomial of degree n. a) Prove that B(f) = (f, f', f",..., f(n)) is a basis for Pn(C), where f(k) is the kth derivative of f. b) Let f = (x – 1)*, and find the matrices 8() Ia and aIBf), where a = (1, x, x2, x) is the standard basis for P3 (C).