2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66122An optimum solution free from degeneration is found to the system of linear algebraic equations with empirical coefficients and right-hand sides. The quadratic risk of estimators of the unknown solution vector is minimized over a class of linear systems with given square norm of the coefficient matrix and length of the right-hand side vector. Empirical coefficients and right-hand sides are assumed to be independent and normal with known variance. It is found that the optimal estimator has the form of a regularized minimum square solution with an extension multiple. A simple formula is derived showing explicitly the dependence of the minimal risk on parameters.Probability15A52text