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 = R4, W is the set of all (x1, x2, x3, x4) such that r1 = 23.
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 = R4, W is the set of all (x1, x2, x3, x4) such that r1 = 23.
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 a
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0ce6604-416c-4f1e-88a9-0dc789d0b227%2F24caefa5-227b-4bf0-ba37-ce1a0ce2d0b6%2Fto4nv8s_processed.jpeg&w=3840&q=75)
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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