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Which of the following sets is not a subspace in the vector space R^3? a.) {((a+b,a-b,2a+b)) | a, b ∈ R} b.) {((a,2a,a)) | a ∈ R} c.) {((a,b,c) ∈ R^3 | a - b - c = 1} d.) {(a,b,c) ∈ R^3 | a = 0, b = 3c} e.) {(a,b,c) ∈ R^3 | 2a = 3c}

Which of the following sets is not a subspace in the vector space R^3? a.) {((a+b,a-b,2a+b)) | a, b ∈ R} b.) {((a,2a,a)) | a ∈ R} c.) {((a,b,c) ∈ R^3 | a - b - c = 1} d.) {(a,b,c) ∈ R^3 | a = 0, b = 3c} e.) {(a,b,c) ∈ R^3 | 2a = 3c}

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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Which of the following sets is not a subspace in the vector space R^3? a.) {((a+b,a-b,2a+b)) | a, b ∈ R} b.) {((a,2a,a)) | a ∈ R} c.) {((a,b,c) ∈ R^3 | a - b - c = 1} d.) {(a,b,c) ∈ R^3 | a = 0, b = 3c} e.) {(a,b,c) ∈ R^3 | 2a = 3c}

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