The multivariate Dixon resultant formulation has been shown by Kapur and Saxena to implicitly exploit the sparse structure of a polynomial system in computing their resultants (or more precisely, projection operators). It is shown how the construction for generating a Dixon resultant matrix from a polynomial system can be modified to generate instead a sparse resultant matrix. An algorithm for constructing a sparse resultant matrix for a polynomial system is given. Unlike the sparse resultant matrix construction algorithms by Canny and Emiris, the proposed algorithm does not explicitly use the support of the polynomial system in its construction. This algorithm is empirically and theoretically compared with the subdivision and incremental methods by Canny and Emiris.