Matrix light-curve inversion (MLI) is a technique for deducing the surface brightness distributions of rapidly rotating spotted stars or the surface albedo distributions of planets (in particular Pluto) from their rotational light curves. When applied to the stellar problem, it has the significant advantage over ``spot models'' that it makes no a priori assumptions about the number of spots on the stellar surface or their shapes. We demonstrate the viability of MLI for determining the locations and sizes of dark spots on stellar surfaces and explore its potential and its limitations by presenting the results of inversions of synthetic light curves corresponding to model stars with known surface features. We show that when light curves acquired through different photometric filters are simultaneously inverted, significant improvements can be achieved compared to when only a single filter is used. In particular, it becomes possible to detect the presence of high-latitude activity, presenting the possibility of corroborating Doppler images that imply high-latitude spots.