Help with Wronskians and matricies?

[hxtasy]

http://www.math.ucdavis.edu/~lai/22b/handouts/Wronskian.pdf

*[edit]wrong link

I am working off this example. First off I think there is a typo in it, in the second example y1'' should be two, can someone confirm this because at the moment i am losing my mind?


My question is how or what order do you add these things? in a 2x2 matrix type wronskian I can see from the example that you start with the first row first column, take that and "draw a diagonal line" down to the second column 2nd row, you take the product of these. Then you take the first column second row and draw an up arrow, take the product of these, then take the sum of these two but the second product is going to be a negative sum.




Ok I can get the 2x2's but what about the 3x3s? what is the pattern for this? I'm not even going to try to guess because i keep getting it wrong. Also you pretty much are checking to see if the answer is non zero, and i think in most cases in a 2x2 if you screw up the arrows you still get an answer to the question is it zero or not, (ie the answer is 6 one way, but if you do the arrows the other way the answer is -6). One time on a test i did the arrows the wrong way and was still able to determine if it was non zero (linearly independent) but the teacher marked my technique wrong because i did the arrows the wrong way.




Could someone pleasae explain this to me? I think there must be a substantial piece of memory in my brain missing if I am supposed to know this from early algebra, i know how to add matrices but is a Wronskian tool technically a matrix??


Thanks for any input.

 

[sutupidmath]

yep, $$y_1''=2$$ it is a typo in there.

 

[sutupidmath]

well, you need to have a look on the determinants of the matrices, and see how you go about solving them. There are different methods, there is triangle method, the method using minors, and also the diagonal method, or how is that called in english. it depends whichever one u find easier to work with. then if you have a square matrix of a rank of 4x4, then you can either perform some elementary transformations to bring it up to a more simpler form, or you can apply the minor methods right away, but sometimes doing so may lead to a lot of calculations, so always it is better to perform elementary transformations.