Revised Cramer's rule for solving linear systems

摘要

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.