1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Linear transformations

  1. Feb 3, 2004 #1
    Let g(x) belonging to Pn-1(R) be an arbiitrary polynomial of degree n-1 or less. Show that there exists a polynomial f(x) belonging to Pn(R) such that xf''(x)-f'(x)=g(x)"

    I interpreted this question as having to prove the linear transformation T: Pn(R) --> Pn-1(R) where f(x) |--> xf''(x)-f'(x) is onto.

    If I let f(x)=a+bx+cx^2+...+zx^n

    Therefore the range of T is {x} which has dimension 1. By the dimension theorem (and just looking at the results), the nullspace has dimension n. This of course is not onto.

    I think I must be interpreting the question wrong. Please help! I have a midterm tomorrow.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted