1. This question is about subspaces and bases. Let H₁R be the hyperplane defined in normal form by and H₂ CR¹ the hyperplane defined in normal form by 0. Let A = H₁nH₂≤R and B = H₁U H₂ ≤R4. Determine whether each of the subsets A and B are subspaces or not. If they are subspaces, prove it using the definition and find a basis; if not, explain why.
1. This question is about subspaces and bases. Let H₁R be the hyperplane defined in normal form by and H₂ CR¹ the hyperplane defined in normal form by 0. Let A = H₁nH₂≤R and B = H₁U H₂ ≤R4. Determine whether each of the subsets A and B are subspaces or not. If they are subspaces, prove it using the definition and find a basis; if not, explain why.
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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