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Prove the following result using the definition of subspace: Let (V,+,.) be a vector space over real number, R and W ⊆ V. Suppose that  i) W ≠ Ø ; and ii) For every w, u ∈ W and every k, m  ∈ real number, R, ku + mw  ∈ W. Then W is a subspace of V.

Prove the following result using the definition of subspace: Let (V,+,.) be a vector space over real number, R and W ⊆ V. Suppose that  i) W ≠ Ø ; and ii) For every w, u ∈ W and every k, m  ∈ real number, R, ku + mw  ∈ W. Then W is a subspace of V.

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
Section4.3: Subspaces Of Vector Spaces
Problem 49E
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Prove the following result using the definition of subspace:

Let (V,+,.) be a vector space over real number, R and W ⊆ V. Suppose that 

i) W ≠ Ø ; and

ii) For every w, u ∈ W and every k, m  ∈ real number, R, ku + mw  ∈ W.

Then W is a subspace of V.

 

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