Remember::NEED HANDWRITTEN SOLUTION then take picture of it.Kindly solve it with Step by step Approach to get like otherwise i will dislike it . KINDLY SEND ME SOLUTION ASAP . THANKYOU 4. Let T : P2 → R³, where P2 = {at² + bt + c : a,b, c € R}, be defined by%3D[p(1)]T(p) = | P(1)F(1)]Here p'(t) is the derivative of the polynomial p(t).(a) Show that T is linear.(b) Find a basis for the null space (kernel) of T.(c) Find a basis for the range of T.(d) Is T one-to-one?(e) Is T onto?

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Answered: 4. Let T: P2→ R°, where P = {at² + bt…

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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Remember::NEED HANDWRITTEN SOLUTION then take picture of it. Kindly solve it with Step by step Approach to get like otherwise i will dislike it . KINDLY SEND ME SOLUTION ASAP . THANKYOU

4. Let T : P2 → R³, where P2 = {at² + bt + c : a,b, c € R}, be defined by
%3D
[p(1)]
T(p) = | P(1)
F(1)]
Here p'(t) is the derivative of the polynomial p(t).
(a) Show that T is linear.
(b) Find a basis for the null space (kernel) of T.
(c) Find a basis for the range of T.
(d) Is T one-to-one?
(e) Is T onto?

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