What Is the Dimension of the Vector Subspace Spanned by e^x and e^2x?

[Pearce_09]

The functions e^x and e^2x
I have to find the dimension of the vector subspace spanned by this set.
Im not sure where to start, I do know how to solve other problems asking the same question just different function. Any help would be greatly appreciated.
thanks
a.p

 

[matt grime]

Firstly this can only make sense if you specify over what field this is a vector space. Stating what the vectort space is would be good. DOesn't make the question any easier or harder but would be a good practice for you to get into.

Assume we mean C(R) the vector space of real valued functions (over R) then you have to vectors e^x and e^2x. They span a space of at most dimension two. Are they linearly independent (as funtions)? Ie are the real numbers u and v such that ue^x+ve^2x is the zero vector in the vector space. Hopefully you know what the zero vector is and see that obviously these are linearly independent vectors