Consider linear transformation T: M22 → P3 defined byT([4]) = (a + b)x³ + (b + c)x² + (c+d)x+ (d+a).(a) Find a basis of ker T and a basis of im T.(b) Let S : P3 → R be the linear transformation defined as S(p(x)) = p(0).Find a basis of ker(SoT) and show that SoT is onto.

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Answered: Consider linear transformation T: M22 →…

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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Consider linear transformation T: M22 → P3 defined by T ([ª d]) = (a + b)2²³ + (b + c)2² + (c + d)x + (d + a). (a) Find a basis of ker T and a basis of im T. (b) Let S : P3 → R be the linear transformation defined as S(p(x)) = p(0). Find a basis of ker(SoT) and show that SoT is onto.