Re: Strange empty set of solutions

*To*: mathgroup at smc.vnet.net*Subject*: [mg71813] Re: Strange empty set of solutions*From*: José Carlos Santos <jcsantos at fc.up.pt>*Date*: Thu, 30 Nov 2006 06:05:03 -0500 (EST)*References*: <ekh7pg$sgs$1@smc.vnet.net> <ekjfnl$d13$1@smc.vnet.net>

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}} Geometrically, this is a straight line in space which passes through the origin. Such a line as *obviously* two points {a,b,c} with norm 1 (those points are symmetric with respect to the origin, of course). You can even do the computation by hand: if you want to get the points {a,b,c} such that 1) a = 0.0410026 c; 2) b = 1.35294 c; 3) a^2 + b^2 + c^2 = 1 then these points are +/-{0.0243644,0.803937,0.594215}. Best regards, Jose Carlos Santos