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Math Help - Determinants (using elementary row operations)

  1. #1
    ebb
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    Determinants (using elementary row operations)

    Hi, if anyone could explain how you get from
    (x+y+z+t)det 1 1 1 1
    qqqqqqqqqqq y z t x
    qqqqqqqqqqq z t x y
    qqqqqqqqqqq t x y z

    to
    (x+y+z+t)det 0 1 1 1
    qqqqqqqqqq (y-z+t-x) z t x
    qqqqqqqqqq (z-t+x-y) t x y
    qqqqqqqqqq (t-x+y-z) x y z
    that would be brilliant! Totally confused
    PS. The qs are just in there to make the matrices slightly more lined up (spaces don't seem to work)! Ignore the qs
    Last edited by ebb; July 17th 2012 at 06:18 AM.
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  2. #2
    ebb
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    Re: Determinants (using elementary row operations)

    I figured that step out but I am stuck again :/
    The original question was: find
    det x y z t
    ---- y z t x
    ---- z t x y
    ---- t x y z
    as a product of linear factors

    We end up with
    (x+y+z+t)(x-y+z-t)det (t-y-z+x) 2(x-z)
    ----------------------- (y-t) --- (y+z-t-x)
    Which is easy enough to solve I thought...
    BUT, they give the final answer as -(x+y+z+t)(x+iy-z-it)(x-y+z-t)(x-iy-z+it)
    WHERE DID THE iS COME FROM? Madness. Help please!
    Last edited by ebb; July 17th 2012 at 06:37 AM.
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