Assume thát B is a basis for an finite-dimensional inner product space V, and let a E V. Prove that if (a, b) = 0 for all b E B, then a = 0.
Assume thát B is a basis for an finite-dimensional inner product space V, and let a E V. Prove that if (a, b) = 0 for all b E B, then a = 0.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.5: Basis And Dimension
Problem 69E: Find a basis for R2 that includes the vector (2,2).
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![3. Assume that B is a basis for an finite-dimensional inner product space V, and let a E V. Prove that if
(a, b) = 0 for all b E B, then a = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7abbf2d5-6ef3-489c-b2da-4d9327a88b2a%2F919bc20f-1380-4d69-8aa6-0e2188fabec3%2Fm13g35h_processed.png&w=3840&q=75)
Transcribed Image Text:3. Assume that B is a basis for an finite-dimensional inner product space V, and let a E V. Prove that if
(a, b) = 0 for all b E B, then a = 0.
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