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Problem 12. Let U, W be subspaces of V. (a) Prove that UC W if and only if Wº CUº. (b) Prove that (U+W)⁰ = UºnWº. (c) Prove (UnW)⁰ = Uº + Wº.

Problem 12. Let U, W be subspaces of V. (a) Prove that UC W if and only if Wº CUº. (b) Prove that (U+W)⁰ = UºnWº. (c) Prove (UnW)⁰ = Uº + Wº.

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.CM: Cumulative Review
Problem 5CM: Take this test to review the material in Chapters 4 and 5. After you are finished, check your work...
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Problem 12. Let U, W be subspaces of V. (a) Prove that UC W if and only if W⁰ C Uº. (b) Prove that (U+W)⁰ = Uºnwº. (c) Prove (UnW)⁰ = Uº + Wº.
Transcribed Image Text:Problem 12. Let U, W be subspaces of V. (a) Prove that UC W if and only if W⁰ C Uº. (b) Prove that (U+W)⁰ = Uºnwº. (c) Prove (UnW)⁰ = Uº + Wº.
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