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Math Help - Factorization Method

  1. #1
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    Factorization Method

    Question : Solve the equations
    2x + 3y+z=9
    x+2y+3z=6
    3x+y+2z=8
    by factorization method
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  2. #2
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    I don't know of the method you are speaking of but you can solve it as follows


     <br />
\left[ \begin{array}{c}<br />
x\\<br />
y\\<br />
z\end{array}\right]=\left[ \begin{array}{ccc}<br />
2 & 3 & 1 \\<br />
1 & 2 & 3 \\<br />
3 & 1 & 2 \end{array} \right]^{-1} \left[ \begin{array}{c}<br />
9\\<br />
6\\<br />
8\end{array}\right]<br />
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  3. #3
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    Thanks but what should i do next ????

    Quote Originally Posted by pickslides View Post
    I don't know of the method you are speaking of but you can solve it as follows


     <br />
\left[ \begin{array}{c}<br />
x\\<br />
y\\<br />
z\end{array}\right]=\left[ \begin{array}{ccc}<br />
2 & 3 & 1 \\<br />
1 & 2 & 3 \\<br />
3 & 1 & 2 \end{array} \right]^{-1} \left[ \begin{array}{c}<br />
9\\<br />
6\\<br />
8\end{array}\right]<br />

    Thanks Pickslides but i dont know what should i do next with that the method u posted does it have a method which i could sees on how to solve that problem ...
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  4. #4
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    To finish with the method posted you need to find this

     <br />
\left[ \begin{array}{ccc}<br />
2 & 3 & 1 \\<br />
1 & 2 & 3 \\<br />
3 & 1 & 2 \end{array} \right]^{-1} <br />

    which is the inverse of a 3\times 3 matrix, read this
    Cramer's rule - Wikipedia, the free encyclopedia

    the result needs to be mulitplied by

     \left[ \begin{array}{c}<br />
9\\<br />
6\\<br />
8\end{array}\right]

    do you know how to multiply matrices?

    Read this, Matrix multiplication - Wikipedia, the free encyclopedia

    or try this Matrix Multiplying Calculator

    Good luck!
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  5. #5
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    Thanks mate........

    Quote Originally Posted by pickslides View Post
    To finish with the method posted you need to find this

     <br />
\left[ \begin{array}{ccc}<br />
2 & 3 & 1 \\<br />
1 & 2 & 3 \\<br />
3 & 1 & 2 \end{array} \right]^{-1} <br />

    which is the inverse of a 3\times 3 matrix, read this
    Cramer's rule - Wikipedia, the free encyclopedia

    the result needs to be mulitplied by

     \left[ \begin{array}{c}<br />
9\\<br />
6\\<br />
8\end{array}\right]

    do you know how to multiply matrices?

    Read this, Matrix multiplication - Wikipedia, the free encyclopedia

    or try this Matrix Multiplying Calculator

    Good luck!


    Thanks mate for helping me with this one .............. cheers mate
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  6. #6
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    Quote Originally Posted by zorro View Post
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  7. #7
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    Cheers mite

    Quote Originally Posted by pickslides View Post
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  8. #8
    Super Member Bacterius's Avatar
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    Just couldn't resist
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