Linear Independence of Functions & The Wronskian

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What is the analog of Linear Independence for functions? If this was just vectors linear independence would mean the only way you can take a linear combination that adds up to zero is the trivial linear combination with all the coefficients being zero. Same for functions. However, we do have one extra tool called the Wronskian, which is a nifty little determinant that we can use to create a quick test for linear dependence of a set of functions. The connection to differential equations will be that we will be looking for a fundamental set of solutions which will have to be linearly independent, more on that in the next video.

0:00 2D case
1:22 Geometric Picture
2:27 Linear Independence
5:54 The Wronskian
8:37 Example

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Видео Linear Independence of Functions & The Wronskian канала Dr. Trefor Bazett