Given that f is a polynomial of degree n in Pn, show that { f, f', f'', . . . , f(n)} is a basis for Pn. ( f(k) denotes the kth derivative of f.)
Given that f is a polynomial of degree n in Pn, show that { f, f', f'', . . . , f(n)} is a basis for Pn. ( f(k) denotes the kth derivative of f.)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.3: Orthonormal Bases:gram-schmidt Process
Problem 71E
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Given that f is a polynomial of degree n in Pn, show that { f, f', f'', . . . , f(n)} is a basis for Pn. ( f(k) denotes the kth derivative of f.)
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