7. In the vector space L(R²), let T be the transformation defined byaaT(d) = (c-30 d-36)3aa. Is T linear?b. Does there exist a 2x2 matrix A such that AB = T(B) for all 2x2 matrices B?c. Does there exist a 2x2 matrix A such that BA = T(B) for all 2x2 matrices B?

a)To determine if the transformation T is linear, we need to check if it satisfies two properties:…

Answered: 7. In the vector space L(R²), let T be…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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7. In the vector space L(R²), let T be the transformation defined by a a T (ª d ) = (c −² 3a b - 3a d - 3b a. Is T linear? b. Does there exist a 2x2 matrix A such that AB = T(B) for all 2x2 matrices B? c. Does there exist a 2x2 matrix A such that BA = T(B) for all 2x2 matrices B?