Minimal free resolutions for subschemes of star configurations

We study some subschemes of a star configuration whose support is defined in a combinatorial way. On the other hand we study some schemes arising from special square matrices. We see that in many important cases such subschemes coincide with the previous subschemes of a star configuration. This permits to give a graded minimal free resolution for them, getting in a special case a Gorenstein scheme of codimension 3.