Let u = (u₁, ₂) and v = (v₁, v₂) be vectors in R². Consider an inner product in R² defined by theformula(u, v) = 21v₁ - U₁V2 − U2V₁ + U2V2.i. Show that R2 with the above defined inner product is a real inner product space.ii. Find the distance between vectors u = (2, 1) and v = (1, 2) using the inner product definedabove.

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Let u = (₁, ₂) and v = (v₁, V₂) be vectors in R². Consider an inner product in R2 defined by the formula (u, v) = 201₁ - U₁ V2 — U2V₁ + U2V2. i. Show that R²2 with the above defined inner product is a real inner product space. ii. Find the distance between vectors u = (2, 1) and v= (1,2) using the inner product defined above.

Let u = (₁, ₂) and v = (v₁, V₂) be vectors in R². Consider an inner product in R2 defined by the formula (u, v) = 201₁ - U₁ V2 — U2V₁ + U2V2. i. Show that R²2 with the above defined inner product is a real inner product space. ii. Find the distance between vectors u = (2, 1) and v= (1,2) using the inner product defined above.

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 87E

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