Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Cramer's Rule

Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_186

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.

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© Kluwer Academic Publishers 2001

Authors and Affiliations

  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege PartUSA
  2. 2.School of Information Technology & EngineeringGeorge Mason UniversityFairfaxUSA