y11 try to do all the question 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 samebut the null-space and left null-space are different?

Answered: Image /qna-images/answer/ee52717f-c856-4379-b8c3-19b34a5beecf.jpg

. What is the projection of v=e₁ +2e2 − 3e3 on H : x₁ + 2x2 + 4x4 = 0? . Let V be a subspace of Rn. Then show that dim V = n − 1 if and only if V for some a 0. . (T) Does there exist a real matrix A, for which, the Row space and column

. What is the projection of v=e₁ +2e2 − 3e3 on H : x₁ + 2x2 + 4x4 = 0? . Let V be a subspace of Rn. Then show that dim V = n − 1 if and only if V for some a 0. . (T) Does there exist a real matrix A, for which, the Row space and column

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.6: The Algebra Of Matrices

Problem 13E

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Question

y11 try to do all the question

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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