Re: help create a unique solution system
- To: mathgroup at smc.vnet.net
- Subject: [mg27635] Re: help create a unique solution system
- From: "Andre Giroux" <giroux at dms.umontreal.ca>
- Date: Fri, 9 Mar 2001 02:35:49 -0500 (EST)
- Organization: Sympatico
- References: <9850ep$5jr@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi Mc.
Here is a solution.
It is based on a theorem of Hadamard according to which a matrice a[[i,j]]
is non-singular provided that
|a[[i,i]] | > sum |a[[i,j]]| for each row i.
\!\(\(n = 5;\)\n
\(offDiag =
Table[If[i == j,
0, \(\((\(-1\))\)\^Random[Integer]\) Random[Integer, {1, 20}]],
{i,
n}, {j, n}];\)\n
\(onDiag =
Table[\(\((\(-1\))\)\^Random[Integer]\)
Random[Integer, {\[Sum]\+\(j = 1\)\%n Abs[
offDiag[\([\)\(i, j\)\(]\)]] +
1, \[Sum]\+\(j = 1\)\%n Abs[offDiag[\([\)\(i, j\)\(]\)]] +
20}], {i, n}];\)\n
matrice =
Table[If[i == j, onDiag[\([\)\(i\)\(]\)] + offDiag[\([\)\(i, j\)\(]\)],
offDiag[\([\)\(i, j\)\(]\)]], {i, n}, {j, n}]\)
The setting up of the equations once the coefficient matrice is known is
left as an exercise ;-) .
"cdes" <cdes43 at videotron.ca> a écrit dans le message news:
9850ep$5jr at smc.vnet.net...
> Could someone help me create a unique solution system of 5 random linear
> equations with 5 unknown x1, x2, x3, x4, x5, with integer coefficients
> (different from zero) and second members integers (all different from
zero).
> Thanks in advance,
> Mc
> kaoum at videotron.ca
>
>
>