  In this paper we construct free resolutions of certain class of closed
subvarieties of affine space of symmetric matrices (of a given size). Our class
covers the symmetric determinantal varieties (i.e., determinantal varieties in
the space of symmetric matrices), whose resolutions were first constructed by
J\'ozefiak-Pragacz-Weyman. Our approach follows the techniques developed in
Free Resolutions of Some Schubert Singularities by
Kummini-Lakshmibai-Sastry-Seshadri, and uses the geometry of Schubert
varieties.
