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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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