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Making the Jacobi Matrix

  1. Mar 26, 2012 #1
    1. The problem statement, all variables and given/known data

    The transformation f is defined by: R^2 --> R^2 and is defined by:
    f(x,y) = (y^5, x^3)

    Find the jacobi matrix and its determinant

    2. Relevant equations

    f(x,y) = (y^5, x^3)

    3. The attempt at a solution

    I would start by differentiating y^5 with respect to x and then y, then differentiate x^3 with respect to x and then y.

    I end up with:

    Df = (0.......... 5y^4 )
    ........(3x^2...... 0 )

    And from here I dont know what to do. Usually I would be told, that Df = (2,1) for example, and then I would place them instead of y and x, but here Im not given any other information than what I have written above. How do I find the determinant?
     
  2. jcsd
  3. Mar 26, 2012 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    How about just doing what you were told to do? Yes, if you were asked to find the Jacobian matrix and its determinant at, say, (1, 2) you would replace x and y with those. But you aren't asked to do that so just leave them as "x" and "y".
     
  4. Mar 27, 2012 #3
    Okay, thank you.

    But I have another question, what is the difference between the Jacobi Matrix and the Jacobi determinant?
     
  5. Mar 27, 2012 #4
    I am also asked to:

    let D be the set of points (x,y) in R^2 doe which 0 ≤ x ≤ 1 and

    0 ≤ y ≤ 1. Find a function g: R^2 --> R for which

    1010 h(x,y)dxdy =
    1010 h(y5, x3*g(x,y)dxdy

    is true for all functions h: D --> R integrable over D
     
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