       Re: Solutions that are not solutions

• To: mathgroup at smc.vnet.net
• Subject: [mg32082] Re: Solutions that are not solutions
• From: Tom Burton <tburton at cts.com>
• Date: Sat, 22 Dec 2001 04:22:59 -0500 (EST)
• References: <9vuth9\$of2\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hello,

This system of equations contains only four nontrivial equations (the rest being tautologies)

t + a y == t + z
u + v == v + a y
a u + w == w + a z
2
t u y - w y  - u x z + v y z == 1

Furthermore, only two of the first three are linearly independent, yielding by inspection u == z == ay.  Hence the warning from the solver that not all variables are found. You need to supplement solution 1 with the additional specification y==0.

Tom Burton

On Fri, 21 Dec 2001 08:57:13 +0000 (UTC), in comp.soft-sys.math.mathematica you 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}}

Tom Burton

```

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