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Math Help - Matrix Help

  1. #1
    Newbie
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    Oct 2009
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    Matrix Help

    I need some help solving these two problems. Thank you.




    1. 5x-3y=14
    -x+2y=10




    2. 2x+y=21
    3x-2y-2z=4
    -x-y-z=5
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  2. #2
    Senior Member Stroodle's Avatar
    Joined
    Jun 2009
    Posts
    367
    For the first one you can use the matrices:

    \begin{bmatrix} 5 & -3\\ -1 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}=  \begin{bmatrix}<br />
14 \\ 10\end{bmatrix}

    Then multiply both sides of the equation by the inverse of the 2x2 matrix:

    \begin{bmatrix} x \\ y \end{bmatrix}= \begin{bmatrix}\frac{2}{7} & \frac{3}{7}\\ \frac{1}{7}&\frac{5}{7}\end{bmatrix}  \begin{bmatrix}<br />
14 \\ 10\end{bmatrix}

    \begin{bmatrix} x \\ y \end{bmatrix}=  \begin{bmatrix}\frac{58}{7} \\ \frac{64}{7} \end{bmatrix}

    The same process can be used for the second question
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