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System of linear equations

  1. Feb 14, 2007 #1
    1. The problem statement, all variables and given/known data

    is every system of 6 equations and 5 unknowns consistent?

    I think that not every one is consistent because after Gaussian elimination you may arrive at equation where 0=1, but I want a sure confirmation.
    Thanks
     
  2. jcsd
  3. Feb 14, 2007 #2
    What does it mean for a system of linear equations to be consistent? Does your answer agree with the definition?
     
  4. Feb 14, 2007 #3

    radou

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    Homework Helper

    A trivial example:

    x1 + x2 + x3 + x4 + x5 = 1
    x1 + x2 + x3 + x4 + x5 = 0
    x1 + x2 + x3 + x4 + x5 = 0
    x1 + x2 + x3 + x4 + x5 = 0
    x1 + x2 + x3 + x4 + x5 = 0
    x1 + x2 + x3 + x4 + x5 = 0

    Does this system have a solution?

    Edit: I forgot to add the 6th equation. The question remains unchanged.
     
    Last edited: Feb 14, 2007
  5. Feb 14, 2007 #4
    thanks.
    ps: sorry, perhaps I made a mistake: 6 equations IN 5 unknowns.
     
  6. Feb 14, 2007 #5

    HallsofIvy

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    That was what everyone assumed you meant, that is what radou gave.
     
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