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For each of the following subsets of R", determine whether it is a subspace of R" or not a) S = {(x₁, x2, x3) € R³|2x₁-3x₂ + x3 = 0} E b) Q = {(x₁, x2, x3, x4) € R¹ | x₁ = 3x3 and x₂ = 4x4 }

For each of the following subsets of R", determine whether it is a subspace of R" or not a) S = {(x₁, x2, x3) € R³|2x₁-3x₂ + x3 = 0} E b) Q = {(x₁, x2, x3, x4) € R¹ | x₁ = 3x3 and x₂ = 4x4 }

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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For each of the following subsets of R", determine whether it is a subspace of R" or not a) S = {(x₁, X2, X3) € R³|2x₁-3x₂ + x3 = 0} E b) Q = {(x₁, x2, x3, x4) E R¹ | x₁ = 3x3 and x₂ = 4x4}
Transcribed Image Text:For each of the following subsets of R", determine whether it is a subspace of R" or not a) S = {(x₁, X2, X3) € R³|2x₁-3x₂ + x3 = 0} E b) Q = {(x₁, x2, x3, x4) E R¹ | x₁ = 3x3 and x₂ = 4x4}
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