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MathGroup Archive 2004

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Re: 5 variables Guass isnt working, matrix solution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50465] Re: 5 variables Guass isnt working, matrix solution
  • From: "Dr. Wolfgang Hintze" <weh at snafu.de>
  • Date: Sun, 5 Sep 2004 03:53:41 -0400 (EDT)
  • References: <chbm20$rnt$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Roger,

things normally don't work if you're not using correct Mathematica 
syntax. Using it there's no problem solving your set of equations with 
standard methods.

Here we go

1) Your equations (notice: the * can be replaced by a space)

In[10]:=
eq1 = 5*a - c - d - e == 0.5;
eq2 = 4*b - c - e == 1;
eq3 = 6*c - a - b - d - e == 1;
eq4 = 4*d - a - c == 1;
eq5 = 5*e - a - b - c == 1.5;

2) more conveniently written as a list

In[15]:=
eq = {eq1, eq2, eq3, eq4, eq5}

Out[15]=
{5*a - c - d - e == 0.5, 4*b - c - e == 1,
   -a - b + 6*c - d - e == 1, -a - c + 4*d == 1,
   -a - b - c + 5*e == 1.5}

3) Now solving (and taking the first solution, btw. there is only one)

In[16]:=
s = First[Solve[eq]]

Out[16]=
{a -> 0.41304347826086957, c -> 0.5,
   d -> 0.47826086956521746, b -> 0.5217391304347826,
   e -> 0.5869565217391304}

4) Test if solution is correct

eq /. s

{True, True, True, True, True}

ok.

5) The solution must also be rational. Here we go to get this representation

In[21]:=
Rationalize[s]

Out[21]=
{a -> 19/46, c -> 1/2, d -> 297089030890994/
     621186155499351, b -> 12/23, e -> 27/46}

Regards,
Wolfgang

roger wrote:

> 5a-c-d-e  =0.5
> 4b-c-e    =1
> 6c-a-b-d-e=1
> 4d-a-c    =1
> 5e-a-b-c  =1.5
> 
> Solve for a,b,c,d, and e.   Guass inversion isnt working.
> 
> Maybe a matrix solution.
> 
> 


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