Let R=k[T1,…,Tf] be a standard graded polynomial ring over the field k and Ψ be an f×g matrix of linear forms from R , where 9d415df51087d17bbd6fde17af4" title="Click to view the MathML source">1≤g<f. Assume 889517dcc166518dcdf"> is 0 and that e6d60803c8d81e4"> is exactly one short of the maximum possible grade. We resolve , prove that 907f1fa708b"> has a e4934ce635a44" title="Click to view the MathML source">g-linear resolution, record explicit formulas for the h -vector and multiplicity of 907f1fa708b">, and prove that if e6afcef3d4dcbaf6d992b896bd2" title="Click to view the MathML source">f−g is even, then the ideal 9d4d73bbaa62" title="Click to view the MathML source">Ig(Ψ) is unmixed. Furthermore, if e6afcef3d4dcbaf6d992b896bd2" title="Click to view the MathML source">f−g is odd, then we identify an explicit generating set for the unmixed part, a8eef666ba672c758d7de8245" title="Click to view the MathML source">Ig(Ψ)unm, of 9d4d73bbaa62" title="Click to view the MathML source">Ig(Ψ), resolve R/Ig(Ψ)unm, and record explicit formulas for the h -vector of R/Ig(Ψ)unm. (The rings R/Ig(Ψ) and 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.