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## Homework Statement

f1 = 0 , f2 = x , f3 = e^x

I am supposed to find out if these are linearly independent or dependent. Just by looking at it, I can't see a way to write one of the functions as a combination of the other two with constant multiples, so to make sure that it is linearly independent, I used the Wronskian

f1' = 0 f2' =1 f3'= e^x

f1" = 0 f2"=0 f3" = e^x

So I evaluated the determinant of

0 x e^x

0 1 e^x

0 0 e^x

And that equals zero, which would mean to me that the functions are linearly dependent. I'm not sure how that could be. Any thoughts?