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

Mar 2016
2
0
Kingston
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?math info.png
 

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chiro

MHF Helper
Sep 2012
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Australia
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.