# Revised Cramer's rule for solving linear systems

Author Affiliations

^{1}Department of Mathematics, College of Natural and Computational Science, Assosa University, Assosa, Ethiopia

*Res. J. Mathematical & Statistical Sci.,* **Volume 6, Issue (7),** Pages 1-4, July,12 **(2018)**

## Abstract

In this paper, it has been tried to revise the Cramer's rule for solving systems of linear equations and a new version, called revised Cramer's rule for solving linear systems is formulated. The revised Cramer's rule is formulated by starting with basic ideas of Cramer's rule and combining them with the transpose of the coefficient matrices. While Cramer's rule is based on column wise replacement of the coefficient matrix by the column vector of the right side constants, the revised Cramer's rule is based on the row replacement of the transpose of the coefficient matrix by the transpose of the column vector of the right side constants. The proof of the revised Cramer's rule for solving linear systems is also attempted and the working rule for the revised Cramer's rule is given. Numerical solution is obtained for the new version and its application to Electrical networks is incorporated. The result yielded that the revised Cramer's rule can be used for solving systems of linear equations as another method.

## References

- Haward Anton and Chris Rorrs (2010)., Elementary Linear Algebra: Applications version., John Wiley & Sons 10th edition.
- Ron Larson and David C. Falvo (2009)., Elementary Linear Algebra., Houghton Mifflin Harcourt Publishing Company, 6th edition.
- David Poole (2006)., Linear Algebra - A modern Introduction., Thomson Brooks/ Cole, 2nd edition.
- Bernard Kolman and David R. Hill (2008)., Elementary Linear Algebra with Applications., Pearson Education, Inc. 9th edition.
- Babarinsa O. and Kamarulhaili H. (2017)., Modification of cramer's rule., Journal of Fundamental and Applied Sciences, 9(5), 556-567.
- Nicholson W. Keith (1995)., Linear Algebra with applications., University of Calgary, 3rd edition.
- Meyer C.D. (2000)., Matrix analysis and applied linear algebra., Siam, 71.
- Kenneth Hoffman and Ray Kunze (1971)., Linear Algebra., University of Calgary, 2nd edition.
- Gilbert Strang (1988)., Linear Algebra and its Applications., Massachusetts Institute of Technology, 3rd edition.
- Kreyzig E. (2005)., Advanced Engineering Mathematics., Wiley, 9, edition.