Let 9316302708&_mathId=si1.gif&_user=111111111&_pii=S0021869316302708&_rdoc=1&_issn=00218693&md5=da33e040a2a67cab0d86a0551e241aaa" title="Click to view the MathML source">R=k[T1,…,Tf] be a standard graded polynomial ring over the field k and Ψ be an 9316302708&_mathId=si17.gif&_user=111111111&_pii=S0021869316302708&_rdoc=1&_issn=00218693&md5=d837ebf25b79345f1f0758fe51975dcf" title="Click to view the MathML source">f×g matrix of linear forms from R , where 9316302708&_mathId=si3.gif&_user=111111111&_pii=S0021869316302708&_rdoc=1&_issn=00218693&md5=9f6d19d415df51087d17bbd6fde17af4" title="Click to view the MathML source">1≤g<f. Assume 9316302708&_mathId=si4.gif&_user=111111111&_pii=S0021869316302708&_rdoc=1&_issn=00218693&md5=bd7f97c23acbb889517dcc166518dcdf">9316302708-si4.gif"> is 0 and that 9316302708&_mathId=si21.gif&_user=111111111&_pii=S0021869316302708&_rdoc=1&_issn=00218693&md5=df71cd7ce3d4e8236e6d60803c8d81e4">9316302708-si21.gif"> is exactly one short of the maximum possible grade. We resolve 9316302708&_mathId=si6.gif&_user=111111111&_pii=S0021869316302708&_rdoc=1&_issn=00218693&md5=08fee340632b4bd4f0c63d7ab5435dd2">9316302708-si6.gif">, prove that 9316302708&_mathId=si151.gif&_user=111111111&_pii=S0021869316302708&_rdoc=1&_issn=00218693&md5=55cf7177acd17daabddc0907f1fa708b">9316302708-si151.gif"> has a 9316302708&_mathId=si186.gif&_user=111111111&_pii=S0021869316302708&_rdoc=1&_issn=00218693&md5=a42d4c1f99ce9716017e4934ce635a44" title="Click to view the MathML source">g-linear resolution, record explicit formulas for the h -vector and multiplicity of 9316302708&_mathId=si151.gif&_user=111111111&_pii=S0021869316302708&_rdoc=1&_issn=00218693&md5=55cf7177acd17daabddc0907f1fa708b">9316302708-si151.gif">, and prove that if 9316302708&_mathId=si9.gif&_user=111111111&_pii=S0021869316302708&_rdoc=1&_issn=00218693&md5=767bee6afcef3d4dcbaf6d992b896bd2" title="Click to view the MathML source">f−g is even, then the ideal 9316302708&_mathId=si10.gif&_user=111111111&_pii=S0021869316302708&_rdoc=1&_issn=00218693&md5=a0c5f1cf3205f50b662e9d4d73bbaa62" title="Click to view the MathML source">Ig(Ψ) is unmixed. Furthermore, if 9316302708&_mathId=si9.gif&_user=111111111&_pii=S0021869316302708&_rdoc=1&_issn=00218693&md5=767bee6afcef3d4dcbaf6d992b896bd2" title="Click to view the MathML source">f−g is odd, then we identify an explicit generating set for the unmixed part, 9316302708&_mathId=si11.gif&_user=111111111&_pii=S0021869316302708&_rdoc=1&_issn=00218693&md5=ca7b776a8eef666ba672c758d7de8245" title="Click to view the MathML source">Ig(Ψ)unm, of 9316302708&_mathId=si10.gif&_user=111111111&_pii=S0021869316302708&_rdoc=1&_issn=00218693&md5=a0c5f1cf3205f50b662e9d4d73bbaa62" title="Click to view the MathML source">Ig(Ψ), resolve 9316302708&_mathId=si13.gif&_user=111111111&_pii=S0021869316302708&_rdoc=1&_issn=00218693&md5=c922511c33b1157a15298174313ccbbb" title="Click to view the MathML source">R/Ig(Ψ)unm, and record explicit formulas for the h -vector of 9316302708&_mathId=si13.gif&_user=111111111&_pii=S0021869316302708&_rdoc=1&_issn=00218693&md5=c922511c33b1157a15298174313ccbbb" title="Click to view the MathML source">R/Ig(Ψ)unm. (The rings 9316302708&_mathId=si14.gif&_user=111111111&_pii=S0021869316302708&_rdoc=1&_issn=00218693&md5=d4edb59f81e78f7be3171bfe270d7f12" title="Click to view the MathML source">R/Ig(Ψ) and 9316302708&_mathId=si13.gif&_user=111111111&_pii=S0021869316302708&_rdoc=1&_issn=00218693&md5=c922511c33b1157a15298174313ccbbb" title="Click to view the MathML source">R/Ig(Ψ)unm automatically have the same multiplicity.) These results have applications to the study of the blow-up algebras associated to linearly presented grade three Gorenstein ideals.