ould you please help me answer this question: Show that each of the following are not inner products on R3: a) ⟨u,v⟩ = u1v1 + u2v2 b) ⟨u,v⟩ = u1v2u3 + v1u2v3 for u = (u1, u2, u3)T & v = (v1, v2, v3

ould you please help me answer this question: Show that each of the following are not inner products on R3: a) ⟨u,v⟩ = u1v1 + u2v2 b) ⟨u,v⟩ = u1v2u3 + v1u2v3 for u = (u1, u2, u3)T & v = (v1, v2, v3

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.2: Inner Product Spaces

Problem 94E

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Question

Could you please help me answer this question:

Show that each of the following are not inner products on R³:

a) ⟨u,v⟩ = u₁v₁+ u₂v₂

b) ⟨u,v⟩ = u₁v₂u₃ + v₁u₂v₃

for u = (u₁, u₂, u₃)^T & v = (v₁, v₂, v₃)^T.

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