  In this paper we propose a model for computing a minimal free resolution for
ideals of the form $I_{1}(X_{n}Y_{n})$, where $X_{n}$ is an $n\times n$
skew-symmetric matrix with indeterminate entries $x_{ij}$ and $Y_{n}$ is a
generic column matrix with indeterminate entries $y_{j}$. We verify that the
model works for $n=3$ and $n=4$ and pose some statements as conjectures.
Answering the conjectures in affirmative would enable us to compute a minimal
free resolution for general $n$.
