  Let $\u_{1\times n}$, $\X_{n\times n}$, and $\v_{n\times 1}$ be matrices of
indeterminates, $\Adj \X$ be the classical adjoint of $\X$, and $H(n)$ be the
ideal $I_1(\u\X)+I_1(\X\v)+I_1(\v\u-\Adj \X)$. Vasconcelos has conjectured that
$H(n)$ is a perfect Gorenstein ideal of grade $2n$. In this paper, we obtain
the minimal free resolution of $H(n)$; and thereby establish Vasconcelos'
conjecture.
