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6. Suppose V is a real inner product space. (a) Show that if u, v € V with ||u|| = ||v||, then u + v is orthogonal to u – v. (b) Provide an example of a real inner product space V and u, v Є V such that u + v is not orthogonal to u - v.

6. Suppose V is a real inner product space. (a) Show that if u, v € V with ||u|| = ||v||, then u + v is orthogonal to u – v. (b) Provide an example of a real inner product space V and u, v Є V such that u + v is not orthogonal to u - v.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 37E: Let V be the set of all positive real numbers. Determine whether V is a vector space with the...
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6. Suppose V is a real inner product space. (a) Show that if u, v € V with ||u|| = ||v||, then u + v is orthogonal to u – v. (b) Provide an example of a real inner product space V and u, v Є V such that u + v is not orthogonal to u - v.
Transcribed Image Text:6. Suppose V is a real inner product space. (a) Show that if u, v € V with ||u|| = ||v||, then u + v is orthogonal to u – v. (b) Provide an example of a real inner product space V and u, v Є V such that u + v is not orthogonal to u - v.
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