1. This question is about subspaces and bases. Let H₁ ≤R be the hyperplane defined in normalform by909-and H₂ ≤R¹ the hyperplane defined in normal form byXW= 0.Let A = H₁n H₂≤R¹ and B = H₁U H₂ ≤R4. Determine whether each of the subsets A and B aresubspaces or not. If they are subspaces, prove it using the definition and find a basis; if not,explain why.

Answered: Image /qna-images/answer/7d03f2d0-3966-4791-b02d-94a46725ad83.jpg

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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