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Homework Help: Finding a constant such that system is consistent

  1. Feb 24, 2012 #1
    1. The problem statement, all variables and given/known data
    Screen_shot_2012_02_24_at_1_05_40_PM.png

    3. The attempt at a solution
    So I was thinking of trying to do row reduction in the hopes that would lead me to an answer.

    [itex]\left| \begin{array}{ccc}
    0& 1& 1& 2 \\
    1&1&1&a \\
    1&1&0&2 \end{array} \right| [/itex] → [itex]\left| \begin{array}{ccc}
    1&1&1&a \\
    0&1&1&2 \\
    1&1&0&2
    \end{array} \right| [/itex]→[itex]\left| \begin{array}{ccc}
    1&0&0&a-2 \\
    0&1&1&2 \\
    1&1&0&2
    \end{array} \right| [/itex]→[itex]\left| \begin{array}{ccc}
    1&0&0&a-2 \\
    0&1&1&2 \\
    0&1&0&-a+4
    \end{array} \right| [/itex]→[itex]\left| \begin{array}{ccc}
    1&0&0&a-2 \\
    0&0&1&a-2 \\
    0&1&0&-a+4
    \end{array} \right| [/itex]→[itex]\left| \begin{array}{ccc}
    1&0&0&a-2 \\
    0&1&0&-a+4 \\
    0&0&1&a-2
    \end{array} \right| [/itex]

    So this seems to be telling me that I can choose any [itex]a[/itex] and [itex]x=z=a-2[/itex] and [itex]y=-a+4[/itex]. Am I doing this right?
     
  2. jcsd
  3. Feb 24, 2012 #2

    SammyS

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    Staff Emeritus
    Science Advisor
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    Gold Member

    That all looks fine !
     
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