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Reduced echelon form where all variables seem to = 0

  1. Feb 8, 2010 #1
    1. The problem statement, all variables and given/known data
    Suppose I have the augmented matrix

    0 -1 0 | 0
    0 -6 3 | 0
    0 -1 0 | 0


    2. Relevant equations

    which equates to -y = 0 and -6y + 3z = 0.


    3. The attempt at a solution

    Would the solution be that x, y and z all equal 0?

    Or do I need to let the missing variable, x = s and free variable z = t, so the solution is

    1 0
    s[ 0 ] + t [ 0.5 ]
    0 1

    (even though I know y = 0 and therefore the free variable must(?) be 0 ) ?




    Thanks.
     
  2. jcsd
  3. Feb 8, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Sort of. Yes, definitely y=0 and z=0. And x is free. z isn't.
     
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