For any integer n> 0, let Pn be the vector space of polynomials with at most n degree. Remember that the standard base for Pn is given as B = {1, x, ..., xn}.Let the T: Pn->Pn+1 transform for each p ∈ Pn be defined asT(p)(x) = xp(x)Then the T transformation is a linear transformation. Show. Also find Null and image sets.

I have just used the definitions

Answered: For any integer n> 0, let Pn be the…

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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For any integer n> 0, let Pⁿ be the vector space of polynomials with at most n degree. Remember that the standard base for Pⁿ is given as B = {1, x, ..., xⁿ}.

Let the T: Pⁿ->Pⁿ⁺¹ transform for each p ∈ Pⁿ be defined as

T(p)(x) = xp(x)

Then the T transformation is a linear transformation. Show. Also find Null and image sets.

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