Encyclopedia of Operations Research and Management Science

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

Cramer's Rule

  • Saul I. Gass
  • Carl M. Harris
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.

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Saul I. Gass
    • 1
  • Carl M. Harris
    • 2
  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege PartUSA
  2. 2.School of Information Technology & EngineeringGeorge Mason UniversityFairfaxUSA