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What is the projection of v = ₁ + 2e2 - 3e3 on H: ₁ + 2x₂ + 4x4 = 0? Let V be a subspace of Rn. Then show that dim V = n − 1 if and only if V = {x: a¹x For some a 0. (T) Does there exist a real matrix A, for which, the Row space and column space are 11 11-6 11 1:0 +2

What is the projection of v = ₁ + 2e2 - 3e3 on H: ₁ + 2x₂ + 4x4 = 0? Let V be a subspace of Rn. Then show that dim V = n − 1 if and only if V = {x: a¹x For some a 0. (T) Does there exist a real matrix A, for which, the Row space and column space are 11 11-6 11 1:0 +2

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
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 67E: Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many...
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3. What is the projection of v = e₁1 + 2e2 − 3e3 on H : x₁ + 2x2 + 4x4 = 0? 4. Let V be a subspace of Rn. Then show that dim V = n − 1 if and only if V = {x : a¹x = 0} for some a 0. 5. (T) Does there exist a real matrix A, for which, the Row space and column space are same but the null-space and left null-space are different?
Transcribed Image Text:3. What is the projection of v = e₁1 + 2e2 − 3e3 on H : x₁ + 2x2 + 4x4 = 0? 4. Let V be a subspace of Rn. Then show that dim V = n − 1 if and only if V = {x : a¹x = 0} for some a 0. 5. (T) Does there exist a real matrix A, for which, the Row space and column space are same but the null-space and left null-space are different?
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