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Homework Statement
Let V = {f: [tex]\mathbb {R}\rightarrow\mathbb {R}[/tex]} be the vector space of functions. Are f1 = ex, f2 = e-x (both [tex]\in[/tex] V) linearly independent?
Homework Equations
0 = aex + be-x Does a = b = 0?
The Attempt at a Solution
My first try, I put a = e-x and b = -ex. He handed it back and told me to try again. I think the problem was that my a and b were not constants. But how to prove that there are no constants that will make the equation 0? I wrote some stuff down about the fact that, if a=0, then b = 0 (and the converse). Is that sufficient or am I way off?