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