Let R=k[T1,…,Tf] be a standard graded polynomial ring over the field k and Ψ be an e51975dcf" title="Click to view the MathML source">f×g matrix of linear forms from R , where bbd6fde17af4" title="Click to view the MathML source">1≤g<f. Assume bb889517dcc166518dcdf"> is 0 and that e4"> is exactly one short of the maximum possible grade. We resolve , prove that has a e4934ce635a44" title="Click to view the MathML source">g-linear resolution, record explicit formulas for the h -vector and multiplicity of , and prove that if baf6d992b896bd2" title="Click to view the MathML source">f−g is even, then the ideal bbaa62" title="Click to view the MathML source">Ig(Ψ) is unmixed. Furthermore, if baf6d992b896bd2" title="Click to view the MathML source">f−g is odd, then we identify an explicit generating set for the unmixed part, ba672c758d7de8245" title="Click to view the MathML source">Ig(Ψ)unm, of bbaa62" title="Click to view the MathML source">Ig(Ψ), resolve 98174313ccbbb" title="Click to view the MathML source">R/Ig(Ψ)unm, and record explicit formulas for the h -vector of 98174313ccbbb" title="Click to view the MathML source">R/Ig(Ψ)unm. (The rings R/Ig(Ψ) and 98174313ccbbb" 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.