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Thread: For the system of equations check whether the 2 conditions in IMF theorem are true

  1. #1
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    Question For the system of equations check whether the 2 conditions in IMF theorem are true

    For the system of equations check whether the 2 conditions in IMF theorem are true-math.png
    For the system of equations below, check whether the two conditions in the Implicit
    Function Theorem are satisfied at point A = (x, y, t) = (1, 1, 0), where x and y are
    variables and t is a parameter. If yes, find the expression for &dx/&dt and evaluate it at A.

    EQ#1 xy2 − y = 5t

    EQ#2 2yt = x3 – 1

    Pretty confused as to where to start, i think it may involve a jacobian matrix however?For the system of equations check whether the 2 conditions in IMF theorem are true-math-info.png
    Attached Thumbnails Attached Thumbnails For the system of equations check whether the 2 conditions in IMF theorem are true-1002696_10205635220340696_2893048776214084322_n.jpg  
    Last edited by taocruze; Mar 15th 2016 at 04:39 PM.
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  2. #2
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    Re: For the system of equations check whether the 2 conditions in IMF theorem are tru

    Hey taocruze.

    The Jacobian is a determinant of a matrix. It has a specific formula for a 2x2 matrix which you should learn.

    Getting the matrix involves finding the partial derivatives and you need to specify the transformation from your first set to your second set when that is involved.

    If the matrix is zero then an inverse function doesn't exist in the neighborhood of that point.
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