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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

    none

    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

    CompuChip

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    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?
    ...
     
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