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(b) = R°, W is the set of all (x1, 22, 13) such that 2xi = -x2+ X3. (c) V = R³, W is the set of all (x1, x2, x3) such that x1 + x2+ x3 = -1.

(b) = R°, W is the set of all (x1, 22, 13) such that 2xi = -x2+ X3. (c) V = R³, W is the set of all (x1, x2, x3) such that x1 + x2+ x3 = -1.

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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please send handwritten solution for Q 3 part c
3. In the following either prove that the set W is a subspace of the vector space V or give a counterex- ample to show that it is not. (a) V = Rª, W is the set of all (x1, x2, x3, x4) such that x1 = x3. (b) V = R³, W is the set of all (x1, x2, x3) such that 2x1 = -x2 + x3. %3D (c) V = R³, W is the set of all (x1, x2, x3) such that x1 + x2+ x3 = -1.
Transcribed Image Text:3. In the following either prove that the set W is a subspace of the vector space V or give a counterex- ample to show that it is not. (a) V = Rª, W is the set of all (x1, x2, x3, x4) such that x1 = x3. (b) V = R³, W is the set of all (x1, x2, x3) such that 2x1 = -x2 + x3. %3D (c) V = R³, W is the set of all (x1, x2, x3) such that x1 + x2+ x3 = -1.
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