Answered: Show that the function defines an inner…

Show that the function defines an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2, v3). ⟨u, v⟩ = 2u1v1 + 3u2v2 + u3v3

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 12EQ

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Question

Show that the function defines an inner product on R³, where u = (u₁, u₂, u₃) and v = (v₁, v₂, v₃).

⟨u, v⟩ = 2u₁v₁ + 3u₂v₂ + u₃v₃

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