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MathGroup Archive 2006

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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


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