Let T: V→ V be a linear transformation. A subspace WV is T-invariant if: T(W) CW. Prove the followingsubspaces are T-invariant.1. {0} CV2. V3. Image(T)4. ker(T)

Given that T:V→V be a linear transformation .A subspace W⊆V T is T- invariant if T(W)⊆W.

Answered: Kis T-invariant if. T(W) W

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Kis T-invariant if. T(W) W

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.3: Matrices For Linear Transformations

Problem 52E: Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.

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Question

Let T: V→ V be a linear transformation. A subspace WV is T-invariant if: T(W) CW. Prove the following
subspaces are T-invariant.
1. {0} CV
2. V
3. Image(T)
4. ker(T)

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