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Math Help - [SOLVED] Guass-Jordan find all solutions of sys of equations

  1. #1
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    [SOLVED] Guass-Jordan find all solutions of sys of equations

    I have to use Gauss-Jordan elimination, put in reduced row echelon form and find all solutions to the following system of equations

    2x - 3y - 8z = 7
    -2x + 2z - w = -7
    x - y - 3z + w = 6

    I end up in RRE form

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

    I think

    x = 3 + z
    y = -1 - 2z
    z = ???
    w = 3

    How can I solve the system?
    Last edited by thekrown; March 7th 2010 at 03:25 PM.
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  2. #2
    Super Member Deadstar's Avatar
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    There are infinitely many solutions but your RRE should be

    1 0 -1 0 | 2
    0 1 2 0 | -1
    0 0 0 1 | 3
    Last edited by Deadstar; March 7th 2010 at 04:52 PM.
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  3. #3
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    I need to be more careful with my calculations. I almost had it.

    So the system has infinitely many solutions because at least one variable is a free variable and can be anything.
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  4. #4
    Super Member Deadstar's Avatar
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    Quote Originally Posted by thekrown View Post
    I need to be more careful with my calculations. I almost had it.

    So the system has infinitely many solutions because at least one variable is a free variable and can be anything.
    Yeah, to see this just set w to be any number then you can solve it as there will be 3 equations, 3 unknowns. Change w, the rest of the solutions change, change w an infinite number of times, infinite number of solutions.

    Look up Diophantine equations for similar things. (not sure how they work with systems of equations though)
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