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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
>
>
>



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