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differentiating determinants...

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    I don't really understand what you want to do. Find the determinant of both those matrices, and then do the derviatives on the left hand side, and you should come out with that identity it gives you. Do you not know how to do a determinant? Or do you not know how to differentiate?
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    (Original post by Worzo)
    I don't really understand what you want to do. Find the determinant of both those matrices, and then do the derviatives on the left hand side, and you should come out with that identity it gives you. Do you not know how to do a determinant? Or do you not know how to differentiate?
    i just keep going wrong. oh well, i'll keep trying. there's one more i'm stuck on...

    a triangle is formed by the lines a_1 x + b_1 y + c_1 = 0, a_2 x + b_2 y + c_2 = 0, a_3 x + b_3 y + c_3 = 0. show the area of the triangle = Δ^2 / 2C_1.C_2.C_3

    where C_n denotes the cofactor of c_n
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    For your original question, I find the determinant to be:

    yz^2 - zy^2 - xz^2 + zx^2 + xy^2 - yx^2

    So finding the partial derivative WRT y, gives

    z^2 - 2zy +2xy - x^2

    Then finding the partial derivative WRT x gives

    2y - 2x

    Which you can put back into matrix format.

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Updated: August 11, 2006
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