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Math Help - referring to Chris's DE Tutorial Post # 4 Ex 11

  1. #1
    Senior Member bugatti79's Avatar
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    referring to Chris's DE Tutorial Post # 4 Ex 11

    Hi Folks,

    I was looking at Chris's brill tutorial particularly the Wronskian in example 11 post # 4.

    Hes seems to have taken the (1,1) times the determinant - (2,1) times the determinant +(3,1) times the determinant.

    Is this equivalent to (1,1) times the determinant -(1,2) times the determinant +(1,3) times the determinant?

    Thanks
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  2. #2
    MHF Contributor

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    Well, the "determinants" would be different but, yes, you can expand a determinant along any row or column.
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  3. #3
    Senior Member bugatti79's Avatar
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    Quote Originally Posted by HallsofIvy View Post
    Well, the "determinants" would be different but, yes, you can expand a determinant along any row or column.
    I see, so with a bit of vision he chose the first column because it would be algebraically easier? Thanks
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  4. #4
    A Plied Mathematician
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    In this case, Chris's choice is a good one, because he might get some cancellation going on fairly early in the process, which is what happened. Looking at the symmetries of that particular Wronskian, it seems like the first column is the way to go. Normally, I would pick the row or column that has the most zeros in it, but with a Wronskian, you're unlikely to have zeros.
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