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)
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)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question

Transcribed Image Text: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)

Transcribed Image Text:(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)
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