(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

2. Relevant equations

0 = ae^{x}+ be^{-x}Does a = b = 0?

3. 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?

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# Linear Algebra: Linear Combinations

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