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The goal of this paper is to propose a fast and reliable method of simultaneous estimation of conductivity and electrode contact impedances for a homogeneous 2-D disk. Magic Toeplitz matrix as the Neumann-to-Dirichlet map with finite width electrodes plays the central role in our linear model, called the gapZ model. This model enables testing of various hypotheses using the F-test, such as the uniformity of electrode impedances and their statistical significance. The gapZ model is compared with the finite element approximation, and illustrated and validated with a phantom tank experiment filled with saline. Further, this model was illustrated with the patient breast EIT data to identify bad contact electrodes.