       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)

```Use exact numbers until the end.

c = Cos[Sqrt];

s = Sin[Sqrt];

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

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

---- "JosÃ© 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/Sqrts, 2/5(1 - c)},
>       {2/5(1 - c), -1 + s/Sqrt, 4/5 + c/5},
>       {-2s/Sqrt, -c, -1 + s/Sqrt}} // N
>
> with c = Cos[Sqrt] and s = Sin[Sqrt].
>
> 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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