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Gaussian Elimination Solve for variable

  1. Sep 28, 2011 #1
    1. The problem statement, all variables and given/known data

    Determine the value of k for which the system
    x + y + 2z = 3
    x + 2y -4z = -3
    2 + 8 + kz = -29
    has no solutions.

    2. Relevant equations
    None

    3. The attempt at a solution
    Converting to a matrix

    1 1 2 3
    1 2 -4 -3
    2 8 k -29

    r2=r2-r1

    1 1 2 3
    0 1 -6 0
    2 8 k -29

    r3=r3-2r1

    1 1 2 3
    0 1 -6 0
    0 6 (k-4) -35

    r3=r3-6r2

    1 1 2 3
    0 1 -6 0
    0 0 (k+32) -35

    So then I figured that:
    (k + 32)z = -35
    k = (-35/z) - 32

    But the problem is I'm doing this online and the solution has to be a real number without variables. So I think I may have gone wrong somewhere. How do I solve for k?
     
  2. jcsd
  3. Sep 28, 2011 #2
    When you have the row: 0 0 (k+32) -35, what does that row mean? You are right when you say (k+32)z=-35. So, what value of k makes this line untrue? (don't move things around, just look at it like this). It's a particular situation you should be familiar with, as it signals when any row reduced matrix has no solution.
     
  4. Sep 30, 2011 #3
    Oh, so (k+32) must equal 0 to make the solution impossible. Which means k = -32?
     
  5. Sep 30, 2011 #4
    You got it :)
     
  6. Sep 30, 2011 #5
    OMG! Ingenious! Thanks guys. Your help is always great!
     
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