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(a) Prove that if W₁ is any subspace of a finite dimenional vector space V, then there exists a subspace W₂ of V such that V=W₁W₂. (b) Let V = R² and W-1 = {(a1,0): a₁ € R} Give two examples of two different subspaces W₂ and W₂ such that V=W₁ W₂ and V=W₁ W₂

(a) Prove that if W₁ is any subspace of a finite dimenional vector space V, then there exists a subspace W₂ of V such that V=W₁W₂. (b) Let V = R² and W-1 = {(a1,0): a₁ € R} Give two examples of two different subspaces W₂ and W₂ such that V=W₁ W₂ and V=W₁ W₂

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) Prove that if W₁ is any subspace of a finite dimenional vector space V, then there exists a subspace W₂ of V such that V = W₁ W2. (b) Let V = R² and W-1 = {(a₁,0): a₁ = R} Give two examples of two different subspaces W₂ and W₂ such that V=W₁ W₂ and V=W₁ W₂
Transcribed Image Text:(a) Prove that if W₁ is any subspace of a finite dimenional vector space V, then there exists a subspace W₂ of V such that V = W₁ W2. (b) Let V = R² and W-1 = {(a₁,0): a₁ = R} Give two examples of two different subspaces W₂ and W₂ such that V=W₁ W₂ and V=W₁ W₂
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