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Question: how to solve without free variable t

Question:how to solve without free variable t

ComputerUser 535 Maple
polynomial
February 24 2013
0 
g1 := x^2-w*y;
g2 := x*y-w*z;
g3 := y^2-x*z;
S12 := SPolynomial(g1, g2, plex(x, y, z, w));
eq1:= S12 = u1*g1 + u2*g2 + u3*g3;
with(LinearAlgebra):
T:=GenerateMatrix([eq1],[u1,u2, u3],augmented);
S:=LinearSolve(T,free=t);

(u1,u2,u3) should be (0,0,-w);
 
the goal is find a u1,u2,u3 to make eq1 equal S12, where u1,u2,u3 should be in terms of x y z w
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