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- Jan 29, 2012

- 661

I have given a link to the topic there so the OP can see my response.Trying to understand the material here. It says that "...the set of solutions is linearly independent on I if and only if W(y1, y2...yn) doesn't = 0 for every x in the interval. (W(y1, y2...yn) being the Wronskian.)

But then I read a comment on youtube: "your first example is wrong, the wronsky is only used to show linear independence. if your determinant is 0 , it doesnt always mean ur your vectors are linear dependent." I guess the wronskian was used for vectors here but I imagine the concept is same for DE's?

So I have this set of functions f1(x) = x, f2(x) = x^2, f3(x) = 4x - 3x^2

and I get the wronskian to = 0. So by the youtuber's comment does this mean these set of functions could either be linearly independent or dependent? How do you determine whether they're independent or dependent?