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Suppose that B = {V₁, V2,..., Vk) is an orthonormal basis for a subspace W of R". Let C be the nx k matrix whose columns are the vectors in B. Prove the following statements: (a) CTC = Ik. (b) Pw = CCT.

Suppose that B = {V₁, V2,..., Vk) is an orthonormal basis for a subspace W of R". Let C be the nx k matrix whose columns are the vectors in B. Prove the following statements: (a) CTC = Ik. (b) Pw = CCT.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 59CR
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75. Suppose that B = {V₁, V₂,V) is an orthonormal basis for a subspace W of R". Let C be the nxk matrix whose columns are the vectors in B. Prove the following statements: (a) CTC = Ik. (b) Pw = CCT.
Transcribed Image Text:75. Suppose that B = {V₁, V₂,V) is an orthonormal basis for a subspace W of R". Let C be the nxk matrix whose columns are the vectors in B. Prove the following statements: (a) CTC = Ik. (b) Pw = CCT.
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