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Math Help - Matrix Inversion Help

  1. #1
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    Matrix Inversion Help

    I'm completely lost with this question. I'mnot exactly sure how to go about doing matrix inversion
    any help is greatly appreciated

    Question:
    A distributor has given three customers a deal on three products. He sold 10 units of product A, 5 units of product B, and 12 units of product C to the first customer for $66. He sold 5, 7, and 10 units of A, B, and C, respectively to the second customer for $54. Finally, the third customer
    received 6 units of each product for $42. Government regulations require that the distributor make individual product prices known and that the prices be the same for all customers. Set up the problem, put it in matrix format, and solve, using matrix inversion, for the implicit prices he charged to his customers.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ihatemath09 View Post
    I'm completely lost with this question. I'mnot exactly sure how to go about doing matrix inversion
    any help is greatly appreciated

    Question:
    A distributor has given three customers a deal on three products. He sold 10 units of product A, 5 units of product B, and 12 units of product C to the first customer for $66. He sold 5, 7, and 10 units of A, B, and C, respectively to the second customer for $54. Finally, the third customer
    received 6 units of each product for $42. Government regulations require that the distributor make individual product prices known and that the prices be the same for all customers. Set up the problem, put it in matrix format, and solve, using matrix inversion, for the implicit prices he charged to his customers.
    The question gives you a set of simultaneous equations:

     <br />
\begin{array}{rrrrrrr}<br />
10a&+&5b&+&12c&=&66\\<br />
5a&+&7b&+&10c&=&54\\<br />
6a&+&6b&+&6b&=&42<br />
\end{array}<br />

    Writing:

     <br />
\bold{A}=\left[\begin{array}{ccc}10&5&12\\5&7&10\\6&6&6\end{array  }\right]<br />

     <br />
\bold{x}=\left[\begin{array}{c}a\\b\\c\end{array}\right]<br />

     <br />
\bold{y}=\left[\begin{array}{c}66\\54\\42\end{array}\right]<br />

    Then our equations can be written:

     <br />
\bold{A}\bold{x}=\bold{y}<br />

    and so:

     <br />
\bold{x}=\bold{A}^{-1}\bold{y}<br />

    So now to complete this you need to invert \bold{A} using whatever methos/s you have been shown and then perform the matrix multiplication.

    The problem from our point of view is we do not know which methods you have been taught for inverting matrices.

    CB
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