Answered: Find linear transformations U, T: F2…

Find linear transformations U, T: F2 --> F2 such that UT =To (the zero transformation) but TU ≠ T0 . Use your answer to find matrices A and B such that AB = 0 but BA ≠ 0.

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

Find linear transformations U, T: F² --> F² such that UT =T_o (the zero transformation) but TU ≠ T₀ . Use your answer to find matrices A and B such that AB = 0 but BA ≠ 0.

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