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A formula for calculating the solution of a nonsingular system of linear equations. Cramer's rule states that the solution of the (n × n) nonsingular linear system Ax = b is xi = detAi(b)/detA, i = 1, ..., n, where detA is the determinant of A, and detAi(b) is the determinant of the matrix obtained by replacing the ith column of A by the right-hand side vector b. This rule is inefficient for numerical computation and its main use is in theoretical analysis. See Matrices and matrix algebra.