       Re: Solutions that are not solutions

• To: mathgroup at smc.vnet.net
• Subject: [mg32077] Re: [mg32049] Solutions that are not solutions
• From: BobHanlon at aol.com
• Date: Sat, 22 Dec 2001 04:22:51 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```In a message dated 12/21/01 4:32:36 AM, psino at tee.gr writes:

>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 only get one solution.

\$Version

"4.1 for Power Macintosh (November 2, 2000)"

X={{0,y,z},{y,x,t},{u,v,w}};
A={{1,1,a},{0,1,0},{0,0,1}};

eqns = {X.A==Transpose[A].X,Det[X]==1};

soln = Flatten[Solve[eqns,{x,y,z,t,u,v,w}]]

{x -> (a*t*y^2 + a*v*y^2 - w*y^2 - 1)/
(a^2*y^2), z -> a*y, u -> a*y}

X /. soln

{{0, y, a*y}, {y, (a*t*y^2 + a*v*y^2 -
w*y^2 - 1)/(a^2*y^2), t},
{a*y, v, w}}

eqns /. soln

{True, True}

Bob Hanlon
Chantilly, VA  USA

```

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