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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
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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