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Math Help - finding equilibrium for a system of equations

  1. #1
    Junior Member
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    Sep 2008
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    finding equilibrium for a system of equations

    I am having problems with a homework problem. I am told for a systems of the form ⃗x = A⃗x + ⃗b to find the equilibrium point. Our textbook does not cover this but my teacher did cover this in class but did not give an example how to do problems like this she just did did proofs with no numbers. I have attached the problem as a jpeg. I was able to find the eigenvalues for each matrix I just am lost in finding the equilibrium for the system. Any help would be appreciated.
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  2. #2
    Super Member
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    Aug 2008
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    Find the values of x and y for which the right side is zero. That's the equilibrium point. A phase portrait of the system is easily drawn in Mathematica:

    Code:
    eqPt =
     Graphics[{PointSize[0.01], Red, Point[{-1, 1/2}]}];
    Show[{StreamPlot[{x + 1, 3 x + 2 y + 2}, {x, -5, 5}, {y, -5, 5}], 
      eqPt}]
    Attached Thumbnails Attached Thumbnails finding equilibrium for a system of equations-aaporta.jpg  
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  3. #3
    Junior Member
    Joined
    Sep 2008
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    thanks for the help! I was not fully understanding the problem because I though it was x instead of x prime. thanks!
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