Existance problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg13741] Existance problem*From*: Joacim Jonsson <d96-jjo at nada.kth.se>*Date*: Wed, 19 Aug 1998 01:38:30 -0400*Sender*: owner-wri-mathgroup at wolfram.com

I have a problem which i need some help with: Does it exists variables x,y,z so that the system a1*x + b1*y + c1*z + d1 >= 0 a2*x + b2*y + c2*z + d2 >= 0 . . an*x + bn*y + cn*z + dn >= 0 is fullfilled? A way to geometrically interpret the problem is that each equation defines a subspace of R3, "sliced out" by a plane, and the equation system is the intersection of all subspaces, and is that intersection an empty set or not!? Another way of putting it: does it exist a point (x,y,z) that lies on the "front" side of all planes?