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Math Help - Solving purely symbolic systems of linear equations

  1. #1
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    Oct 2009
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    Solving purely symbolic systems of linear equations

    Hello,

    I'm working through a finite element text which provides a symbolic solution to a system of linear equations which I suspect might be incorrect based on some checks that I've done. I'm interested in double checking their math, but I'm finding it excessively complicated with the techniques that I know how to use. Here is the system:

    u_i=\alpha_1+\alpha_2 x_i + \alpha_3 y_i
    u_j=\alpha_1+\alpha_2 x_j + \alpha_3 y_j
    u_m=\alpha_1+\alpha_2 x_m + \alpha_3 y_m

    I'm trying to solve for \alpha_1, \alpha_2, \alpha_3.

    First I tried substitution by solving the first equation for \alpha_1 and plugging into the second equation. Then I tried solving that for \alpha_2, etc. The math just got so messy that I gave up.

    I next tried setting up the equations in matrix format:

    <br /> <br />
\left\[\begin{matrix}1&x_i&y_i\\1&x_j&y_j\\1&x_m&y_m\end{  matrix}\right\]<br /> <br />
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  2. #2
    Senior Member yeKciM's Avatar
    Joined
    Jul 2010
    Posts
    456
    a_{11}x_1+a_{12}x_2+ . . . + a_{1n}x_n=b_1
    a_{21}x_1+a_{22}x_2+ . . . + a_{2n}x_n=b_2
    . . . . . . . . . . . . . . . . . . . . . . . . . . . .
    a_{m1}x_1+a_{m2}x_2+ . . . + a_{mn}x_n=b_m

    do for that one u can find determinant and say if this then that, or if something it would be .... and so on...
    or u can use substitution and show how does it work, and in which cases it will have one, more or none solutions ....




    P.S. Sorry, but i didn't see correct... your  x, y are known members ???
    Last edited by yeKciM; August 1st 2010 at 08:31 AM.
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