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8. In the following either show that the set W is a subspace of the vector space V or give a counterexample to show that it is not. (a) V = R³, W is the set of all (x1, X2, T3) such that 2r1 = 3x2. (b) V = R°, W is the set of all (1, X2, 03, X4, 05) Such that 18203 =1. (c) V = R², W is the set of all (x1,x2) such that |c1|| %3D

8. In the following either show that the set W is a subspace of the vector space V or give a counterexample to show that it is not. (a) V = R³, W is the set of all (x1, X2, T3) such that 2r1 = 3x2. (b) V = R°, W is the set of all (1, X2, 03, X4, 05) Such that 18203 =1. (c) V = R², W is the set of all (x1,x2) such that |c1|| %3D

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 56E: Give an example showing that the union of two subspaces of a vector space V is not necessarily a...
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8. In the following either show that the set W is a subspace of the vector space V or give a counterexample to show that it is not. (a) V = R³, W is the set of all (x1, x2, x3) such that 2x1 = 3x2. (b) V = R°, W is the set of all (x1, x2, X3, X4, X5) such that x1x2X3 = 1 (c) V = R², W is the set of all (x1, 82) such that |x1| = |T2|.
Transcribed Image Text:8. In the following either show that the set W is a subspace of the vector space V or give a counterexample to show that it is not. (a) V = R³, W is the set of all (x1, x2, x3) such that 2x1 = 3x2. (b) V = R°, W is the set of all (x1, x2, X3, X4, X5) such that x1x2X3 = 1 (c) V = R², W is the set of all (x1, 82) such that |x1| = |T2|.
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