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I've been doing some home work on Vector Spaces and Vector Subspaces and I need help solving a problem... Can somebody please help me?

Consider the differential equation f'' + 5f' + 6f' = 0 Show that the set of all solutions of this equation is a vector subspace of the vector space of all continuours funtions with the usual operations

How I went about this question is considering the 3 for U to be a vector subspace of V

1. The zero vector has to be in U

2. if r and s are in U, then r+s lies in U

3. if r lies in U, then kr lies in U for all k in R

I know that the zero vector is in U since f'' + 5f' + 6f' = 0 (IT EQUALS 0) however, I dont know how to show the other 2 conitions. (conditions 2 and 3.)

Can somebody PLEASE help me.

Thank you