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Problem 4. For each of the following functions, prove whether or not it defines an inner product on the given vector space. (a) On R2, (8-9)- = ac - bd. (b) On P, (c) On Mnxn, (f(x),9(x)) = [' f'(x)9(x)dx. (A, B) = tr(A + B).

Problem 4. For each of the following functions, prove whether or not it defines an inner product on the given vector space. (a) On R2, (8-9)- = ac - bd. (b) On P, (c) On Mnxn, (f(x),9(x)) = [' f'(x)9(x)dx. (A, B) = tr(A + B).

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College Algebra

College Algebra

1st Edition

ISBN: 9781938168383

Author: Jay Abramson

Publisher: OpenStax

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Transcribed Image Text:Problem 4. For each of the following functions, prove whether or not it defines an inner product on the given vector space. (a) On R2, (8-9)- = ac - bd. (b) On P, (c) On Mnxn, (f(x),9(x)) = [' f'(x)9(x)dx. (A, B) = tr(A + B).

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