Question: Solving system of polynomial equations

Hi! I have a matrix A where the entries

satisfy the conditions in eq1. I set A equal

to the general

4x4 matrix X and convert to a set so that I can 

solve the system of equations for the variables

in A (i.e. solve for a,b,c,d, s,t,r,l). However,

in my program below, I get "res:= "

when the program finishes. Why isn't it

giving me any output? Thanks!

restart;

with(LinearAlgebra):

A := Matrix( [ [a*s, a*t, a*r, a*l],[b*s, b*t, b*r, b*l], 

[c*s, c*t, c*r, c*l], [d*s, d*t, d*r, d*l] ] );

eq1 := a*d = b*c, s*l = t*r;

X := Matrix( [ [x_(11), x_(12), x_(13), x_(14)], [x_(21), x_(22), x_(23), x_(24)], 

[x_(31), x_(32), x_(33), x_(34)], [x_(41), x_(42), x_(43), x_(44)] ] );

U := convert( Equate(A, X), set );

res := SolveTools:-PolynomialSystem(U union {eq1}, 1);