Let V = M₁ (K) be the n x n matrices over a field K and B € V a fixed matrix. Which of the following are subspaces UCV?(a) U = {A = M₁ (K) | BAB = 0}(b) U = {A € M, (K) | ABA = 0}Select one:Yes to bothNo to bothYes to (a), while (b) depends on n, K, B which were not specifiedYes to (a), No to (b)No to (a), Yes to (b)

Answered: Image /qna-images/answer/26b7bf96-968a-447f-91ae-752e4c0d342b.jpg

Let V = M₁ (K) be the n x n matrices over a field K and B € V a fixed matrix. Which of the following are subspaces UCV? (a) U = {A = M₁ (K) | BAB = 0} (b) U = {A € M₁(K)| ABA = 0} Select one: Yes to both No to both Yes to (a), while (b) depends on n, K, B which were not specified Yes to (a), No to (b) No to (a), Yes to (b)

Let V = M₁ (K) be the n x n matrices over a field K and B € V a fixed matrix. Which of the following are subspaces UCV? (a) U = {A = M₁ (K) | BAB = 0} (b) U = {A € M₁(K)| ABA = 0} Select one: Yes to both No to both Yes to (a), while (b) depends on n, K, B which were not specified Yes to (a), No to (b) No to (a), Yes to (b)

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 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...

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