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