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: Need some help on vector space

  1. Apr 23, 2009 #1
    1. The problem statement, all variables and given/known data

    use the subspace theorem to decide if the sets is a real vector space with respect to the usual operation

    the set of all solutions of the homogenous differential equation
    7f''(x) +4f'(x) -6f(x) = 0

    2. Relevant equations


    3. The attempt at a solution

    try to put this second order d.e. into first order matrix system.
    but don't know what to do next.

    how to proof one matrix is under a vector space?
  2. jcsd
  3. Apr 23, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    You don't need to know the solutions. Just check if it's a vector space.
    Is the function that sends every x to 0 a solution?
    If f and g are solutions and r is any number, are (f + g) and r f solutions?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook