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If V3(R) is a vector space and W₁ = {(a,0, c): a, c = R} and W₂ = {(0, b, c): b, c = R} are two subspace of V3(R), then show that V = W₁ + W₂ and V W₁ W₂.

If V3(R) is a vector space and W₁ = {(a,0, c): a, c = R} and W₂ = {(0, b, c): b, c = R} are two subspace of V3(R), then show that V = W₁ + W₂ and V W₁ W₂.

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 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...
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If V3(R) is a vector space and W₁ = {(a, 0, c): a, c = R} and W₂ = {(0, b, c): b, c = R} are two subspace of V3(R), then show that V = W₁ + W₂ and V ‡ W₁ W₂.
Transcribed Image Text:If V3(R) is a vector space and W₁ = {(a, 0, c): a, c = R} and W₂ = {(0, b, c): b, c = R} are two subspace of V3(R), then show that V = W₁ + W₂ and V ‡ W₁ W₂.
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