  An 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.
