1. Apr 23, 2009 #1

   zhfs

   

   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?

    

   zhfs, Apr 23, 2009
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3. Apr 23, 2009 #2

   CompuChip

   

   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?
   ...

    

   CompuChip, Apr 23, 2009

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