Question 2. Let T : V →V and S : V→V be two operators. Let U be a T-invariant and S-invariant subspace. a) Is U a T + S-invariant subspace and a TS-invariant subspace? YES NO b) Assume that TS = ST. Are ker T and ImT S-invariant subspaces? YES NO

Question 2. Let T : V →V and S : V→V be two operators. Let U be a T-invariant and S-invariant subspace. a) Is U a T + S-invariant subspace and a TS-invariant subspace? YES NO b) Assume that TS = ST. Are ker T and ImT S-invariant subspaces? YES NO

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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