1. A method comprising: performing, using a processor, an analysis of a matrix to identify an illegal configuration in a system model, the matrix corresponding to a plurality of numerical equations, a numerical equation corresponding to a component of the system model or a topology equation of the system model, the analysis including: identifying a numerical equation in the plurality of numerical equations, and operating on the matrix to identify the illegal configuration, the illegal configuration being identified based at least on the identified numerical equation being linearly dependent on one or more other equations in the plurality of numerical equations; and producing an indication that the system model contains the illegal configuration.