please send handwritten solution for Q 3 part b 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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. 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 = rž. (b) V = R³, W is the set of all (x1, x2, x3) such that 2x1 =-x2 + x3. (c) V = R³, W is the set of all (x1, 2, x3) such that r1 + x2 + x3 = -1.

. 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 = rž. (b) V = R³, W is the set of all (x1, x2, x3) such that 2x1 =-x2 + x3. (c) V = R³, W is the set of all (x1, 2, x3) such that r1 + x2 + x3 = -1.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 54CR: Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector...

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