5. a) Prove that T is one to one but not onto.b) Attempt to define T-¹: P4 → P3 as in for-mula (1) by setting T-¹ (q) = p if and only ifT(p) = q. What is T-¹(x)? In Exercises 1–6, the linear transformations S, T, andH are defined as follows:S:P3 → P4 is defined by S(p) = p'(0).T:P3 → P4 is defined by T (p) = (x + 2)p(x).H:P4 → P3 is defined by H(p) = p'(x) + p(0).

The linear transformation T:p3→p4 is defined by Tp=x+2px . A function is called one to one if…

Answered: 5. a) Prove that T is one to one but…

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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5. a) Prove that T is one to one but not onto. b) Attempt to define T-¹: P4 → P3 as in for- mula (1) by setting T-¹(q) = p if and only if T(p) = q. What is T-¹(x)?