  We provide conditions and algorithmic tools so as to classify and construct
the smallest possible determinantal formulae for multihomogeneous resultants
arising from Weyman complexes associated to line bundles in products of
projective spaces. We also examine the smallest Sylvester-type matrices,
generically of full rank, which yield a multiple of the resultant. We
characterize the systems that admit a purely B\'ezout-type matrix and show a
bijection of such matrices with the permutations of the variable groups. We
conclude with examples showing the hybrid matrices that may be encountered, and
illustrations of our Maple implementation. Our approach makes heavy use of the
combinatorics of multihomogeneous systems, inspired by and generalizing results
by Sturmfels-Zelevinsky, and Weyman-Zelevinsky.
