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: Vector Subspace Question

  1. Oct 12, 2004 #1


    User Avatar

    Let V be the subspace of F([0,1],R) generated by the functions f1, f2, f3 given by:

    f1(x)=1/(x+1) , f2 (x) = 2-x and f3(x) = x^2

    for all x element of [0,1]. Find a basis of the subspace U of V that consists of all the functions g of V such that g(0) = g(1).


    Ok now the very first question I have is what on earth is g? We have three functions (f1, f2, and f3) so where did this g come from? Secondly, how do I start this question? I've looked in my textbook and lecture notes but there aren't any examples like this one. We only have the really simple vector subspace examples and they didn't really help much. Any suggestions would be greatly appreciated. Thanks :smile:
  2. jcsd
  3. Oct 14, 2004 #2


    User Avatar

    Does nobody know how to do this question at all?
  4. Oct 14, 2004 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Huh? You defined what g is, so why are you asking?

    Any g in U must satisfy


    and since U is a subset of V, g must also satisfy


    where the a's are real numbers. What you will have to figure out is how the condition g(0)=g(1) restricts the possible values of a1, a2 and a3.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook