Determine whether there is linear independence or not Determine if the following set of vectors is linearly independent:
$$S =  \{e^x, e^{2x}\}$$ of continuous functions.
So my problem isn't in not knowing what linearly independence is, it is setting up a linear combination of this form:
$$a_1e^x + a_2e^{2x} = ????$$
What do I set it equal to to determine the coefficients? For example if it was in terms of vectors it would be something like:
$$a_1V_1 + a_2V_2 = (0,0,0,)$$ if I was in $R^3$ for instance.

your matrix will be in a 2x2 form where row 1 is ae^x + be^2x = 0 and row 2 = e^x + 2e^2x =0, you find the determinant by factoring out e^xe^(2x) multiplied by your simplified matrix with (1,1) and (1,2) as rows 1 and 2. Hence determinant is e^xe^(2x)* (2-1)= e^xe^(2x)(1) which is not zero, meaning you have a set of linearly independent vectors.. Sorry it is my first time using this and I dont know how to write properly yet. 
