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