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 August 31st, 2013, 12:12 PM #1 Newbie   Joined: Aug 2013 Posts: 2 Thanks: 0 gauss-ellimination problem Dear All! I have a problem, and I need some help, The problem is: I have a linear equation system as follows: Code: |500 -500 0| | 0 | |F1x| |-500 600 100| * |d2x|=| 0 | |0 -10 100| |d3x| | 5 | I want to calculate the result using gauss ellimination(it is only an example, I'll have to solve large systems), but for that I need "only numbers" on the right side (if im right). How can I transform the matrices to the correct form? Best ragards, Ábel P.s.: I'm sorry if it's totally wrong what i've wrote.
 August 31st, 2013, 02:25 PM #2 Global Moderator   Joined: May 2007 Posts: 6,511 Thanks: 585 Re: gauss-ellimination problem Try to clarify the notation.
 August 31st, 2013, 07:32 PM #3 Math Team   Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407 Re: gauss-ellimination problem Hello, p3n3m! You seem to have: $\begin{vmatrix}500=&-500=&0 \\ \\ -500=&600=&100 \\ \\ 0=&-10=&100 \end{vmatrix}\,\cdot\,\begin{vmatrix}0 \\ \\ d2x \\ \\ d3x \end{vmatrix} \;=\;\begin{vmatrix}F1x \\ \\ 0 \\ \\ 5 \end{vmatrix}$ $\text{W\!hat are }d2x\text{ and }d3x\,? \text{Are they variables?\;We seem to have only two of them.}$ $\text{Is }F1x\,\text{ a constant?}$ $\text{As written, the system has }no\text{ solution.}$
 September 1st, 2013, 12:03 AM #4 Newbie   Joined: Aug 2013 Posts: 2 Thanks: 0 Re: gauss-ellimination problem d2x,d3x anf F1x are all unknowns. I'm pretty sure it has solution: if we calculate the matrix product, we get the following equations: -500 d2x=F1x 600 d2x-100 d3x=0 -100 d2x + 100 d3x =5 from the last 2: 6 d2x= d3x -> d2x=0.01 d3x=0.06 -> f1x= -5 my problem is that I can't use the gauss ellimination because I think F1x is on the wrong side
September 1st, 2013, 12:05 PM   #5
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Re: gauss-ellimination problem

Quote:
 Originally Posted by soroban $\begin{vmatrix}500=&-500=&0 \\ \\ -500=&600=&100 \\ \\ 0=&-10=&100 \end{vmatrix}\,\cdot\,\begin{vmatrix}0 \\ \\ d2x \\ \\ d3x \end{vmatrix} \;=\;\begin{vmatrix}F1x \\ \\ 0 \\ \\ 5 \end{vmatrix}$
Using Matrix product we get

$\begin {cases}
-500 \; * \; d2x=F1x \\
600 \; * \; d2x \; + \; 100 \; * \; d3x=0\\
-10 \; * \; d2x \; + \; 100 \; * \; d3x=5
\end{cases}$

Rearranging we get:

$\begin {cases}
-500 \; * \; d2x \; + \; 0 \; * \; d3x \; - \; F1x=0 \\
600 \; * \; d2x \; + \; 100 \; * \; d3x \; + \; 0 \; * \; F1x=0\\
-10 \; * \; d2x \; + \; 100 \; * \; d3x \; + \; 0 \; * \; F1x=5
\end{cases}$

Which we can transform in this matrix system again.

$\begin{vmatrix}-500=&-1 \\ \\ 600=&100=&0 \\ \\ -10=&100=&0 \end{vmatrix}\,\cdot\,\begin{vmatrix}d2x \\ \\ d3x \\ \\ F1x \end{vmatrix} \;=\;\begin{vmatrix}0 \\ \\ 0 \\ \\ 5 \end{vmatrix}$

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