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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?