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Homework Help: Show consistency of equations

  1. Jun 16, 2009 #1
    1. The problem statement, all variables and given/known data

    Show that the simultanbeous equations




    where k is a constant, are consisten only when k=1.

    3. The attempt at a solution

    Don't know how to start, the determinent of the co-efficient matrix is -9. This means they are independant, which means I cant express multiples of (1) and (2) for (3) right? I tried to get x and y in terms of z, then substitute for (3)... Doesn't work. I need the method.
  2. jcsd
  3. Jun 16, 2009 #2


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    Homework Helper

    Set up the augmented matrix of your system of equations (since the order in which the equations are given is unimportant, you can set things up this way)

    2 & -3 & \hphantom{-}1 & k \\
    6 & -7 & \hphantom{-}2 & 4\\
    6 & -1 & -1 & 7

    Use row operations to reduce this to row reduced echelon form. You'll see why when you reach that form.
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