  The classical multidimensional resultant can be defined as the, suitably
normalized, generator of a projective elimination ideal in the ring of
universal coefficients. This is the approach via the so-called inertia forms or
Tr\"{a}gheitsformen. Using clever substitutions, Mertens and Hurwitz gave a
criterion, for recognizing such inertia forms, which amounts to a linear system
for their numerical coefficients. In this article we explicitly solve this
linear system. We do so by identifying a subset of the available equations
which forms a unitriangular system. The key notion we use is that of
transversal, i.e., a selection of a monomial term in each of the homogeneous
polynomials at hand. We need two such transversals which are disjoint and
extremal, in the sense that they relate to extremizers of a, possibly new,
determinantal inequality for differences of two substochastic matrices. Thanks
to this notion of extremal pair of transversals, we derive an explicit formula
for the coefficients of general multidimensional resultants, as a sum of terms
made of a sign times a product of multinomial coefficients, thereby explicitly
showing they are integer-valued.
