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!

Determine whether the following are Vector Spaces

  1. Apr 10, 2013 #1
    1. The problem statement, all variables and given/known data

    a) The set of real polynomials of [itex]x[/itex] divisible by [itex]x^2 + x + 1[/itex];
    b) The set of differentiable functions of [itex]x[/itex] on [itex][0,1][/itex] whose derivative is [itex]3x^2[/itex]
    c) all [itex]f \in F[0,2][/itex] such that [itex]x \geq |f(x)|[/itex] for [itex]0 \leq x \leq 2[/itex]

    3. The attempt at a solution

    a) Yes, it's a vector space, proven with addition and scalar multiplication

    b) I don't really understand what the question is saying, can someone explain to me? A function that differentiates to [itex]3x^2[/itex] is [itex]x^3[/itex]. Now what?

    c) Same goes for this part, not sure what the question is saying

    Thanks in advanced.
     
  2. jcsd
  3. Apr 10, 2013 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    (b) That is not all the functions that differentiate to ##3x^2##
    (c) Try telling us what you think it's saying so we can see where the confusion lies.
     
  4. Apr 11, 2013 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    f(x)= (2/3)x has the property that x> |f(x)|.

    What about 5f(x)?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted