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Solve this system of equations

  1. Feb 13, 2005 #1
    0a - 2b + 3c = 1
    3a + 6b - 3c = -2
    6a + 6b + 3c = 5

    I got a = 3, b = 3/2, c = -4/3 but the book says that this system is inconsistent. It asks us to use Gauss-Jordan elimination (which I have used on the past 5 or so problems and got all the right answers). I know how to do these, I just don't see where my mistake is. I am probably looking over some very simplistic reason why it is inconsistent... Any help is appreciated.
     
  2. jcsd
  3. Feb 13, 2005 #2
    The numbers you have found are not the solutions of this system , because they don't give correct results, if put in any of the equations of the system. And a solution of any system must give correct results for all the equations, so if you find a solution (a,b,c) this must be a solution for all the equations.
    In your problem you can multiply the second equation with -2 and then add it with the third one(Gauss method). Your system ends up like this:
    | 0a-2b+3c=1 | 0a-2b+3c=1
    | -6a-12b+6c=4 <=>| -6a-12b+6c=4
    | 6a+6b+3c=5 | -6b+9c=9

    the last equation can be written like this: -2b+3c=3
    So if you add the first one and the {[-2b+3c=3] multiplied with -1} you get 0=-2
    This last one is actually this equation : 0a+0b+0c=-2. So the initial system has the same solutions as this system:
    0a+0b+0c=-2
    -6a-12b+6c=4
    -6b+9c=9

    obviously this system is inconsistent, so the initial one is also inconsistent as they are equivalent
     
    Last edited: Feb 13, 2005
  4. Feb 13, 2005 #3

    Integral

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    For us to see your mistake you would have to show us your arithemtic. How many times have you repeated the calculations?
     
  5. Feb 13, 2005 #4

    dextercioby

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    I don't know why you struggled so much,the determinant of the coefficients is zero,therefore,no unique solution.

    Daniel.
     
  6. Feb 13, 2005 #5
    The detrminant of the coefficient matrix is equal to zero. Since the matrix is singular, the system is inconsistent.
     
  7. Feb 13, 2005 #6

    Hurkyl

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    Not always.
     
  8. Feb 13, 2005 #7
    lol thanks guys but I don't know what a determinant is yet (that's chapter 2). I have tried it twice, and have gotten the same result both times...

    EDIT: Thanks for your help guys, but on my 4th attempt, I found it to be inconsistent. I don't know what I did wrong the other way because I did it a different way this time. Anyway, thanks for your help.
     
    Last edited: Feb 13, 2005
  9. Feb 14, 2005 #8
    It's amazing how simple a problem can be the 4th time around.

    If I had a dollar for every simple error like that I've made...
     
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