Re: Strange empty set of solutions

• To: mathgroup at smc.vnet.net
• Subject: [mg71814] Re: Strange empty set of solutions
• From: José Carlos Santos <jcsantos at fc.up.pt>
• Date: Thu, 30 Nov 2006 06:05:04 -0500 (EST)
• References: <ekh7pg\$sgs\$1@smc.vnet.net> <ekjfrf\$d7h\$1@smc.vnet.net>

```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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