Decide which of the following subsets of R are also subspaces of R. If a subset IS a subspace, show it. If a subset is NOT a subspace, explain your reasoning. 1. S ((x.y.0): x.y e R) 2. S ((x,2.y): x, y e R) 3. S ((x.x-3y. y): x.y e R) 4. S ((x.y.xy):x.y € R}

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 56E: Give an example showing that the union of two subspaces of a vector space V is not necessarily a...
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Subset?
Decide which of the following subsets of R are also subspaces of R. If a subset IS a subspace, show
it. If a subset is NOT a subspace, explain your reasoning.
1. S ((x.y.0): x.y e R)
2. S (x,2.y): x, y e R)
3. S ((x.x-3y.y): x,y e R}
4. S ((x.y,xy):x.y € R)
Transcribed Image Text:Decide which of the following subsets of R are also subspaces of R. If a subset IS a subspace, show it. If a subset is NOT a subspace, explain your reasoning. 1. S ((x.y.0): x.y e R) 2. S (x,2.y): x, y e R) 3. S ((x.x-3y.y): x,y e R} 4. S ((x.y,xy):x.y € R)
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