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