Could you just explain why you put "uses VectorCalculus" as oppsed to started the procedure "with(VectorCalculus)"? Does it make any difference or is it purely for aethestic purposes? 

with(ArrayTools):
Operator6:=proc(F::list,G::list,X::list) local P,S;
P:= Jacobian(F,X);
S:= Matrix(Gradient(G,X));
if Size(P,2)=Size(S,1) 
then return P^+ . S;
else return fail;
end if;
end proc;
 

So I have condensed down my lines, however there is some kind of error on G when i run it.