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Need some help on vector space

  • Thread starter zhfs
  • Start date
  • #1
10
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Homework Statement



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

Homework Equations



none

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?
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
4,302
47
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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