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MathGroup Archive 2001

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Solutions that are not solutions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg32049] Solutions that are not solutions
  • From: "PSi" <psino at tee.gr>
  • Date: Fri, 21 Dec 2001 03:57:15 -0500 (EST)
  • Organization: National Technical University of Athens, Greece
  • Sender: owner-wri-mathgroup at wolfram.com

I'm trying to solve a system as follows:
X={{0,y,z},{y,x,t},{u,v,w}}
A={{1,1,a},{0,1,0},{0,0,1}}
Solve[{X.A==Transpose[A].X, Det[X]==1},
{x,y,z,t,u,v,w}]

Mathematica 4.1 gives two solutions:
X1={{0,y,0},{y,x,t},{0,v,-1/y^2}}
and
X2={{0,y,a*y},{y,(a*t*y^2-1+a*v*y^2-w*y^2)/(a*y)^2,t},
{a*y,v,w}}

However, X1 is not a solution:
X1.A-Transpose[A].X1={{0,0,0},{0,0,a*y},{0,-a*y,0}}

Could anybody explain this behaviour?
Thanks
PSi





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