Re: Strange empty set of solutions

• To: mathgroup at smc.vnet.net
• Subject: [mg71873] Re: Strange empty set of solutions
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Fri, 1 Dec 2006 06:22:32 -0500 (EST)
• Organization: The Open University, Milton Keynes, UK
• References: <ekh7pg\$sgs\$1@smc.vnet.net> <ekjfnl\$d13\$1@smc.vnet.net> <ekmdkr\$80m\$1@smc.vnet.net>

```José Carlos Santos wrote:
> On 29-11-2006 8:17, Jean-Marc Gulliet wrote:
>
>>> I have a certain 3 x 3 numerical matrix M. If I type
>>>
>>> Solve[M.{a,b,c}=={0,0,0},{a,b,c}]
>>>
>>> I get
>>>
>>> {{a -> 0. + 0.0410026 c, b -> 0. + 1.35294 c}}
>>>
>>> However, if I type
>>>
>>> Solve[{M.{a,b,c}=={0,0,0},a^2+b^2+c^2==1},{a,b,c}]
>>>
>>> I get the empty set. Why is that?
>> According to the online help, "Solve gives {} if there are no possible
>> solutions to the equations. "
>>
>>> I should get two solutions!
>> Not knowing your matrix M, I cannot tell whether your expectation are
>> legitimate; but here is a simple system that returns several solutions:
>
> Yes you can! Like I said, if I type
>
> Solve[M.{a,b,c}=={0,0,0},{a,b,c}]
>
> I get
>
> {{a -> 0. + 0.0410026 c, b -> 0. + 1.35294 c}}

As written above, M is nothing but a scalar: dot product is not defined
for a scalar.

In[1]:=
Solve[M . {a, b, c} == {0, 0, 0}, {a, b, c}]

Solve::eqf: M.{a, b, c} == {0, 0, 0} is not a well-formed equation. More...

Solve::eqf: M.{a, b, c} == {0, 0, 0} is not a well-formed equation. More...

Out[1]=
Solve[M . {a, b, c} == {0, 0, 0}, {a, b, c}]

Have I omitted anything but the definition of M?

Regards,
Jean-Marc

```

• Prev by Date: Re: Algorithm used by "Reduce" function
• Next by Date: Re: Drawing function with 3 variables in a graph
• Previous by thread: Re: Strange empty set of solutions
• Next by thread: Re: Re: Strange empty set of solutions