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Show consistency of equations

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

    Show that the simultanbeous equations

    [itex]6x-7y+2z=4[/itex]

    [itex]6x-y-z=7[/itex]

    [itex]2x-3y+z=k[/itex]

    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

    statdad

    User Avatar
    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)

    [tex]
    \begin{pmatrix}
    2 & -3 & \hphantom{-}1 & k \\
    6 & -7 & \hphantom{-}2 & 4\\
    6 & -1 & -1 & 7
    \end{pmatrix}
    [/tex]


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