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MathGroup Archive 2006

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Re: Re: Strange empty set of solutions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71844] Re: [mg71814] Re: Strange empty set of solutions
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Fri, 1 Dec 2006 06:21:42 -0500 (EST)
  • Reply-to: hanlonr at cox.net

Use exact numbers until the end.

c = Cos[Sqrt[5]];

s = Sin[Sqrt[5]];

M = {{4/5(c - 1), -2/Sqrt[5]s, 2/5(1 - c)}, 
      {2/5(1 - c), -1 + s/Sqrt[5], 4/5 + c/5}, 
      {-2s/Sqrt[5], -c, -1 + s/Sqrt[5]}};

Solve[{M.{x, y, z} ==0, 
        x^2 + y^2 + z^2 == 1}, {x, y, z}]//N//Chop

{{x -> 0.03101724187965791, y -> -0.7067665564761036, z -> -0.7067665564761036}, 
  {x -> -0.03101724187965791, y -> 0.7067665564761036, z -> 0.7067665564761036}}


Bob Hanlon

---- "José Carlos Santos" <jcsantos at fc.up.pt> wrote: 
> On 29-11-2006 8:19, Jens-Peer Kuska wrote:
> 
> > and we can't read you mind and the memory of your computer
> > so we must imagine a matrix M and write down
> 
> Do you want an example? Here it is:
> 
> M = {{4/5(c - 1), -2/Sqrt[5]s, 2/5(1 - c)},
>       {2/5(1 - c), -1 + s/Sqrt[5], 4/5 + c/5},
>       {-2s/Sqrt[5], -c, -1 + s/Sqrt[5]}} // N
> 
> with c = Cos[Sqrt[5]] and s = Sin[Sqrt[5]].
> 
> If I type
> 
> Solve[{M.{x, y, z} == {0, 0, 0}}, {x, y, z}]
> 
> I get
> 
> {{x -> 0. - 0.0438861 z, y -> 0. + 1. z}}
> 
> but if I type
> 
> Solve[{M.{x, y, z} == {0, 0, 0}, x^2 + y^2 + z^2 == 1}, {x, y, z}]
> 
> then I get the empty set. Why is that?
> 
> Best regards,
> 
> Jose Carlos Santos
> 


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