Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2006
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

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