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  1. #1
    dan
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    Question matrix

    can someone tell me how you take the determinant of a 4X4 and 5X5 matrix

    l a1 a2 a3 a4 a5 l
    l b1 b2 b3 b4 b5 l
    l c1 c2 c3 c4 c5 l
    l d1 d2 d3 d4 d5 l
    l e1 e2 e3 e4 e5 l

    and

    l a1 a2 a3 a4 l
    l b1 b2 b3 b4 l
    l c1 c2 c3 c4 l
    l d1 d2 d3 d4 l

    dan
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  2. #2
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    For a discussion on how to find determinants of any order, please click here to render your computer irrepairable (post #7)
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  3. #3
    Member Glaysher's Avatar
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    I never used cofactors to find determinants of 3 by 3 matrices.

    If I extended my method to 4 by 4 I would get for the matrix:

    a b c d
    e f g h
    i. j. k l
    m n o p

    (afkp + bglm + chin + dejo) - (dgjm + cfip + belo + ahkn)

    Is this correct? If so would I be able to extend it for any square matrix
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  4. #4
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    Quote Originally Posted by Glaysher
    I never used cofactors to find determinants of 3 by 3 matrices.

    If I extended my method to 4 by 4 I would get for the matrix:

    a b c d
    e f g h
    i. j. k l
    m n o p

    (afkp + bglm + chin + dejo) - (dgjm + cfip + belo + ahkn)

    Is this correct? If so would I be able to extend it for any square matrix
    Sadly, I think that method only works for 3x3
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  5. #5
    dan
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    Quote Originally Posted by ThePerfectHacker
    Sadly, I think that method only works for 3x3
    i know that that's true...
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by Glaysher
    I never used cofactors to find determinants of 3 by 3 matrices.

    If I extended my method to 4 by 4 I would get for the matrix:

    a b c d
    e f g h
    i. j. k l
    m n o p

    (afkp + bglm + chin + dejo) - (dgjm + cfip + belo + ahkn)

    Is this correct? If so would I be able to extend it for any square matrix
    Is this not a particular case of Leibniz's formula (see here) ?

    RonL
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  7. #7
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    Quote Originally Posted by CaptainBlack
    Is this not a particular case of Leibniz's formula (see here) ?

    RonL
    But that is not necessary the ideal method. Because then you need to compute whether the premutations are even or odd--> That is time consuming.
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  8. #8
    dan
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    Question

    Quote Originally Posted by CaptainBlack
    Is this not a particular case of Leibniz's formula (see here) ?

    RonL
    you tell me ... I did'nt get half of that explnation...
    dan
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  9. #9
    Grand Panjandrum
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    Quote Originally Posted by dan
    you tell me ... I did'nt get half of that explnation...
    dan
    Yes it is

    RonL
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  10. #10
    Grand Panjandrum
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    Quote Originally Posted by ThePerfectHacker
    But that is not necessary the ideal method. Because then you need to compute whether the premutations are even or odd--> That is time consuming.
    Now if I recall I never said it was the ideal method of computing it.

    Similarly if the discussion was about the quadratic formula, and what
    happens for cubics and quartics, just because I might mention the
    existence of the corresponding formulae does not mean that I recommend
    their use for anything other that as a decorative element for a wall
    paper design

    RonL

    (Oh and it/they may have some use as the machinery in the proof
    of other results)
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  11. #11
    Member Glaysher's Avatar
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    I'm amazed I still remember anything about permutations. So much of the stuff I did at uni has been lost to the void. The formula looks familiar enough for me to think I've seen it before. It would have taken ages to find it though and I hadn't even thought to look. Thanks for satisfying my curiousity.
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