Re: Strange empty set of solutions

• To: mathgroup at smc.vnet.net
• Subject: [mg71791] Re: Strange empty set of solutions
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Wed, 29 Nov 2006 02:56:33 -0500 (EST)
• Organization: The Open University, Milton Keynes, UK
• References: <ekh7pg\$sgs\$1@smc.vnet.net>

```José Carlos Santos wrote:
> Hi all,
>
> 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:

In[1]:=
m = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};

In[2]:=
sol = Solve[m . {a, b, c} == {0, 0, 0}, {a, b, c}]

From In[2]:=
Solve::svars: Equations may not give solutions for all "solve" variables.

Out[2]=
{{a -> c, b -> -2*c}}

In[3]:=
a^2 + b^2 + c^2 == 1 /. sol

Out[3]=
{6*c^2 == 1}

In[4]:=
sol = Solve[m . {a, b, c} == {0, 0, 0} &&
a^2 + b^2 + c^2 == 1, {a, b, c}]

Out[4]=
{{a -> -(1/Sqrt[6]), b -> Sqrt[2/3],
c -> -(1/Sqrt[6])}, {a -> 1/Sqrt[6],
b -> -Sqrt[2/3], c -> 1/Sqrt[6]}}

Regards,
Jean-Marc

```

• Prev by Date: Re: sum of integrals over patial intervals != integral
• Next by Date: Re: Bairstow Method
• Previous by thread: Re: Strange empty set of solutions
• Next by thread: Re: Strange empty set of solutions