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Re: 5 variables Guass isnt working, matrix solution


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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