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MathGroup Archive 2001

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Re: solutions that are not solutions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg32073] Re: [mg32049] solutions that are not solutions
  • From: KCConnolly at aol.com
  • Date: Sat, 22 Dec 2001 04:22:45 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

psino at tee.gr wrote:

>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?

I am still laboring with Mathematica 3.0, which only generates X2.  However, X1 appears to be a re-expression of X2 in the instance where a=0, in which case the second entry in the second row of X2 would be undefined through having 0 in the denominator.  And if a=0, then of course a*y and -a*y are 0, and so X1 is (in that limited instance) a solution.

So X2 is the general solution, and X1 is the solution when X2 is undefined.  Hope that helps.

Kevin Connolly


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