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Math Help - Non-Basic solutions to equations...

  1. #1
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    Non-Basic solutions to equations...

    How would I go about calculating a non-basic solution to something like

    2w + 3z = 6
    2x + 3z = 8
    y + 3z = 7

    I'm guessing my solution is going to be a general solution with a free parameter?
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  2. #2
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    Hello, ZTM1989!

    How would I go about calculating a non-basic solution to something like:

    . . \begin{array}{cccc} 2w + 3z &=& 6 & [1] \\<br />
2x + 3z &=& 8 & [2] \\ y + 3z &=& 7 & [3] \end{array}

    I'm guessing my solution is going to be a general solution with a free parameter?
    You are right!


    \begin{array}{ccccccc}\text{Solve [1] for }w: & w &=& \dfrac{6-3z}{2} \\ \\[-3mm]<br />
\text{Solve [2] for }x: & x &=& \dfrac{8-3z}{2} \\ \\[-3mm] \text{Solve [3] for }y: & y &=& 7 - 3z \\ \\[-2mm]<br />
\text{and we have:} & z&=& z \end{array}


    On the right, replace z with a parameter t.


    And we have: . \begin{Bmatrix}w &=& \dfrac{6-3t}{2} \\ \\[-3mm]x &=& \dfrac{8-3t}{2} \\ \\[-2mm] y &=& 7-3t \\ \\ z &=& t \end{Bmatrix}

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  3. #3
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    Thanks a lot.
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