This is from my text, "Linear Algebra" by Serge Lang, pg 11:(adsbygoogle = window.adsbygoogle || []).push({});

-The two functions e^{t}, e^{2t}are linearly independent. To prove this, suppose that there are numbers a, b such that:

ae^{t}+ be^{2t}=0

(for all values of t). Differentiate this relation. We obtain

ae^{t}+ 2be^{2t}= 0.

Subtract the first from the second relation. We obtain be^{2t}=0, and hence b=0. From teh first relation, it follows that ae^{t}=0, and hence a=0. Hence e^{t}, e^{2t}are linearly independent.

I'm confused as to the "Differentiate this relation". I see it creates a system of equations which can then be used to solve for linear independence, but why does it work?

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# Homework Help: Linear Independence of two functions and differentiation

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