My problem in sagemath is as follows, for simplification , given five polynomials $f_1(x,y,z)=-z-y+x+xy+2xy^2$, $f_2(x,y,z)=-z-y+x+xy$, $f_3(x,y,z)=-2z-y+5x$, $f_4(x,y,z)=z+y$, $f_5(x,y,z)=z$ . How to construct by sage the matrix whose the i-th row is coeffcients of the polynomial $f_i(x,y,z)$ .

I want to get the matrix in the form with respect the lexical order of monomials {z,y,x,xy,xy^2}as
$$begin{pmatrix}
-1 & -1 & 1 & 1 & 2
-1 & -1 & 1 & 1 & 0
-2 & -1 & 5 & 0 & 0
1 & 1 & 0 & 0 & 0
1 & 0 & 0 & 0 & 0
end{pmatrix}$$