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Math Help - Changing this simultaneous equation into matrix form

  1. #1
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    Changing this simultaneous equation into matrix form

    I have got two equations that I need help in changing to matrix format.

    a=(b/(cX))+(b/(dY)) --- (1)
    e=(b/(fX))+(b/(gY)) --- (2)

    I know that the format for simultaneous equation to be solved by matrix got to be in the form of:

    ax+by=c
    dx+ey=f

    but I just can't change the above (1) and (2) into that format..please help. Urgent too.

    only X and Y are unknown. The rest are all just constant. thanks again.
    Last edited by mr fantastic; October 8th 2009 at 06:09 PM. Reason: Merged posts
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  2. #2
    MHF Contributor

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    The problem appears to be that those are not linear equations and so cannot be written as a matrix equation.
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  3. #3
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    Hello, chenxianghao!

    Change this simultaneous equation into matrix form

    . . \begin{array}{cccc}\dfrac{b}{cx} +\dfrac{b}{dy}&=& a & (1) \\ \\[-3mm]<br />
\dfrac{b}{fx}+\dfrac {b}{gy} &=&  e & (2)<br />
\end{array}

    \begin{array}{ccccc}\text{Multiply [1] by }cd\!: & bd\,\dfrac{1}{x} + bc\,\dfrac{1}{y} &=& acd \\ \\[-3mm]<br />
\text{Multiply [2] by }fg\!: & bg\,\dfrac{1}{x} + bf\,\dfrac{1}{y} &=& e\!f\!g \end{array}


    \text{Let: }\:X = \frac{1}{x},\;\;Y = \frac{1}{y}


    \text{Then we have: }\;\;\begin{array}{ccc}bdX + bcY &=& acd \\ bgX + b\!fY &=& e\!fg \end{array}


    Now apply your matrix methods:
    . . solve for X\text{ and }Y
    . . then solve for x\text{ and }y.

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