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This paper presents a rigorous accuracy analysis of the method of auxiliary sources (MAS), when applied to scattering problems. A benchmark, canonical geometry, consisting of a perfectly conducting, infinite, circular cylinder, is chosen for clarity and simplicity. For this particular structure it is shown that the MAS square matrix can be inverted analytically, yielding exact mathematical expressions for the discretization error and the condition number of the pertinent linear system. It is also demonstrated that the error increases very abruptly for source locations associated with the characteristic eigenvalues of the scattering geometry, precisely as predicted in theory. Various plots depict comparisons between analytical and computational data for the boundary condition error, and all occurring discrepancies are fully explained. Among several important results of the analysis, the fundamental MAS question concerning the optimal location of the auxiliary sources is thoroughly investigated and resolved on the grounds of error minimization.