Define T:P, → R3 by T(p(t)) = (p(1), p(0), p(0)), where P, is the set of polynomials of degree at most 2.(A) Determine whether T is a linear transformation or not.(solution)(B) Is T a matrix transformation? If yes, find its standard matrix. If not, explain why not.(solution) (C) Find the kernel of T.(solution)(D) Find a basis and the dimension of the kernel of T.(solution)(E) Find the range of T.(solution)(F) Find a basis and the dimension of the range of T.(solution)(G) Is q(t) = 1–t +t² in the kernel of T?(solution)(H) Find the coordinate vector of (5, 4, 4) relative to your B that you found in (F) above.(solution)

Answered: Image /qna-images/answer/cc22530c-7dbb-4557-935d-6941218e35f5.jpg

Answered: by 7 (p(t, (p(1), p(0), p(0)), where Pz…

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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I only need help with part D. I will rate thank you!
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3x₁ - x₂ [-x₁ + x₂] 1. (i) Show that 7 ([x₂]) = [³ T (ii) Find the matrix representation is a linear transformation. of T relative to the standard basis.
Given the following system of linear equations: Зх, + 4х, 1 2.x, 2х, + X3 -1. 2x, 2х, + 4х, (a) Describe v, A and b if the convention used is y. A = b. (b) Determine the linear transformation T that A represents by the convention (v)T = v · A. (c) Find the standard matrix A' of Tif the convention T(v) = A' -v is used instead.
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by 7 (p(t, (p(1), p(0), p(0)), where Pz iš the šêt öf pólynömiálš öf đégréé ät most 2. (A) Determine whether T is a linear transformation or not. (solution) (B) Is T a matrix transformation? If yes, find its standard matrix. If not, explain why not. (solution)