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August 9th, 2007, 01:49 PM   #1
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Gauss Elimination = Matrix

From the help in a previous thread I discovered that I need to use the Gauss Elimination to solve a system of equations. But I have hit a stumbling block on how to apply what i am trying to solve to this Gauss Elimination (GE) process. I have a set of variables H1....Hn, where only n-1 are active in any one equation, plus variables P1 and P2, where only either P1 or P2 is active in any equation. When I try to solve my equation using the GE process I end up with two unknowns, which doesn't allow me to substitute values into the other equations to come up with a value for each variable.

See example:
n=3

H1+H2+P1 = 0.6
H1+H3+P1 = 0.58
H2+H3+P1 = 0.56
H1+H2+P2 = 0.5

my matrix looks like the following...
(H1 H2 H3 P1 P2 C)
Code:
1 1 0 1 0 0.6
1 0 1 1 0 0.58
0 1 1 1 0 0.56
1 1 0 0 1 0.5
removing the first 1 in the 2nd row I get...
Code:
1 1  0 1 0 .6
0 1 -1 0 0 .02
0 1  1 1 0 .56
1 1  0 0 1 .5
removing the first 1 in the 4th row I get...
Code:
1 1  0 1 0 .6
0 1 -1 0 0 .02
0 1  1 1 0 .56
0 0  0 1 -1 .1
removing the left most 1 in the 3rd row I get...
Code:
1 1  0 1  0 .6
0 1 -1 0  0 .02
0 0  2 1  0  .54
0 0  0 1 -1 .1
The last row still has two unknowns, P1-P2=.1

it looks like I need to have one more row/equation in the system, but I am not sure how to come up with another one. Thoughts? I hope the matrix work is readable, didn't know how to format tables. Hopefully none of the math is wrong, but the key point I am trying to make is that there are still two unknowns. Thoughts?

vr, Xei
Xeifrank is offline  
 
August 9th, 2007, 05:53 PM   #2
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There are two unknowns because you have more variables than equations. The only solution is to pick one variable and write all the other variables in terms of it.

The bottom equation gives P1=P2+.1, and from here, you can find all of the other variables in terms of P2.
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August 9th, 2007, 09:12 PM   #3
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Quote:
Originally Posted by roadnottaken
There are two unknowns because you have more variables than equations. The only solution is to pick one variable and write all the other variables in terms of it.

The bottom equation gives P1=P2+.1, and from here, you can find all of the other variables in terms of P2.
example please.
vr, Xei
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August 10th, 2007, 05:24 AM   #4
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Your own example suffices; just pretend that P2 is a numerical value instead of a variable. The method then works, although the same software can't cope with that pretence.
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