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Let U and W be subspaces of a vector space V such that V = U+W {0} if and only if every vector in V Prove that Un W = can be written uniquely as a linear combination of a vector in U and a vector in W

Let U and W be subspaces of a vector space V such that V = U+W {0} if and only if every vector in V Prove that Un W = can be written uniquely as a linear combination of a vector in U and a vector in W

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
Section4.4: Spanning Sets And Linear Independence
Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...
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= Let U and W be subspaces of a vector space V such that V Prove that Un W {0} if and only if every vector in V can be written uniquely as a linear combination of a vector in U and a vector in W = U + W
Transcribed Image Text:= Let U and W be subspaces of a vector space V such that V Prove that Un W {0} if and only if every vector in V can be written uniquely as a linear combination of a vector in U and a vector in W = U + W
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