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## Homework Statement

Let V = {f: [tex]\mathbb {R}\rightarrow\mathbb {R}[/tex]} be the vector space of functions. Are f

_{1}= e

^{x}, f

_{2}= e

^{-x}(both [tex]\in[/tex] V) linearly independent?

## Homework Equations

0 = ae

^{x}+ be

^{-x}Does a = b = 0?

## The Attempt at a Solution

My first try, I put a = e

^{-x}and b = -e

^{x}. 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?