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1. V=R³ S = {12 :* ER}. 3x Let V be a vector space and S be a subset of V. Determine whether S is a subspace of V. a. S is a subspace of V b. S is not a subspace of V 2. Every vector space has at least 2 subspaces. a. True b. False 3. If V is a vector space and S is a finite set of vectors in V, then some subset of S forms a basis for V a. True b. False

1. V=R³ S = {12 :* ER}. 3x Let V be a vector space and S be a subset of V. Determine whether S is a subspace of V. a. S is a subspace of V b. S is not a subspace of V 2. Every vector space has at least 2 subspaces. a. True b. False 3. If V is a vector space and S is a finite set of vectors in V, then some subset of S forms a basis for V a. True b. False

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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1. V = R³ S = { 12 ER}. : -4 3x Let V be a vector space and S be a subset of V. Determine whether S is a subspace of V. a. S is a subspace of V b. S is not a subspace of V 2. Every vector space has at least 2 subspaces. a. True b. False 3. If V is a vector space and S is a finite set of vectors in V, then some subset of S forms a basis for V a. True b. False
Transcribed Image Text:1. V = R³ S = { 12 ER}. : -4 3x Let V be a vector space and S be a subset of V. Determine whether S is a subspace of V. a. S is a subspace of V b. S is not a subspace of V 2. Every vector space has at least 2 subspaces. a. True b. False 3. If V is a vector space and S is a finite set of vectors in V, then some subset of S forms a basis for V a. True b. False
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