We investigated the matrix mineralogy in primitive EH3 chondrites Sahara 97072, ALH 84170, and LAR 06252 with transmission electron microscopy; measured the trace and major element compositions of Sahara 97072 matrix and ferromagnesian chondrules with laser-ablation, inductively coupled, plasma mass spectrometry (LA-ICPMS); and analyzed the bulk composition of Sahara 97072 with LA-ICPMS, solution ICPMS, and inductively coupled plasma atomic emission spectroscopy. The fine-grained matrix of EH3 chondrites is unlike that in other chondrite groups, consisting primarily of enstatite, cristobalite, troilite, and kamacite with a notable absence of olivine. Matrix and pyroxene-rich chondrule compositions differ from one another and are distinct from the bulk meteorite. Refractory lithophile elements are enriched by a factor of 1.5-3 in chondrules relative to matrix, whereas the matrix is enriched in moderately volatile elements. The compositional relation between the chondrules and matrix is reminiscent of the difference between EH3 pyroxene-rich chondrules and EH3 Si-rich, highly sulfidized chondrules. Similar refractory element ratios between the matrix and the pyroxene-rich chondrules suggest the fine-grained material primarily consists of the shattered, sulfidized remains of the formerly pyroxene-rich chondrules with the minor addition of metal clasts. The matrix, chondrule, and metal-sulfide nodule compositions are probably complementary, suggesting all the components of the EH3 chondrites came from the same nebular reservoir.