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Thread: gaussian elimination - urgent help

  1. #1
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    gaussian elimination - urgent help

    hi,

    im trying to solve a set of equations by guassian elimination,

    i got it this far

    1 0 -1 2 0
    0 1 2 3 0
    0 0 0 0 1

    sorry havent figured out how to use the maths tags yet.
    should i have

    X1 -X3 +2X4 = 0
    X2 + 2X3 + 3X4 = 0

    what about the last row?
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  2. #2
    Super Member Showcase_22's Avatar
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    umm, what are the equations?
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  3. #3
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    Quote Originally Posted by jonbob81 View Post
    hi,

    im trying to solve a set of equations by guassian elimination,

    i got it this far

    1 0 -1 2 0
    0 1 2 3 0
    0 0 0 0 1

    sorry havent figured out how to use the maths tags yet.
    should i have

    X1 -X3 +2X4 = 0
    X2 + 2X3 + 3X4 = 0

    what about the last row?
    wouldn't the last row imply that there are no solutions ?

    Bobak
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  4. #4
    Super Member Showcase_22's Avatar
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    Does the matrix equal anything? (is it a matrix?)

    If it does then we might be able to go somewhere since we'll have the value of one of the unknowns.

    I'm really just speculating since i'm a tad confused.
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  5. #5
    MHF Contributor arbolis's Avatar
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    The last row of the matrix implies that $\displaystyle 0\cdot x_1+0\cdot x_2 +0\cdot x_3 + 0\cdot x_4=1 \Leftrightarrow 0=1$ which is false. Thus the set of equations has no solution.
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  6. #6
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    hi its the following set of equations

    2x1 − x2 + x4 = −1
    −x1 + x2 + 2x3 + x4 = 5
    x1 + 2x3 + 2x4 = 4
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  7. #7
    Super Member Showcase_22's Avatar
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    hmm, this is looking a bit peculiar. I did a little something that went like this:

    The equations we have are:

    $\displaystyle 2x_{1}-x_{2}+x_{4}=-1$------>equation 1)
    $\displaystyle -x_{1}+x_{2}+2x_{3}+x_{4}=5$----->equation 2)
    $\displaystyle x_{1}+2x_{3}+2x_{4}=4$----->equation 3)

    2)-3)= $\displaystyle -2x_{1}-x_{2}-x_{4}=1$
    but 10 is $\displaystyle 2x_{1}-x_{2}+x_{4}=-1$.
    This implies that $\displaystyle x_{1}=x_{4}=0$

    As a result, the equations now become:
    $\displaystyle x_{2}=-1$
    $\displaystyle x_{2}+2x_{3}=5$
    $\displaystyle 2x_{3}=4$ or $\displaystyle x_{3}=2$

    However, the values of $\displaystyle x_{2}$ and $\displaystyle x_{3}$ now conflict with equation two.

    I don't think these equations have solutions....
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