Prove that each of the following formulas for (v. tv) defines an inner product on R3. Verify

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Prove that each of the following formulas for (v. tv) defines an inner product on R3. Verify all the inner product axioms in careful detail:
(a) V1W1 + 2V2w2 + 3v3w3
(b) 4v1w1 + 2 v1w2 + 2v2wi +4v2W2 + V3W3
(C) 2v1wi - 2v1w2 - 2V2W1 + 3v2w2 - v2w3 - v3w2 + 2v3w3
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Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

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