In this paper, we show how to compute, using Fitting ideals, the nonfree locus of the moduli space of arrangements of a rank
3
3
simple matroid, i.e., the subset of all points of the moduli space which parametrize nonfree arrangements. Our approach relies on the so-called Ziegler restriction and Yoshinaga’s freeness criterion for multiarrangements. We use these computations to verify Terao’s freeness conjecture for rank
3
3
central arrangements with up to
14
14
hyperplanes in any characteristic.