Modification of Cramer’s rule

Abstract

While Cramer's rule allows complete substitution of constant terms to the coefficient matrix in the system of linear equations, the modified methods of Cramer's rule consider the constant terms as well as the coefficients of the matrix at the same time. The methods are derived from one of the properties of determinants. Furthermore, we prove the two methods to be equivalent and provide MATLAB codes for the modified methods. However, the methods are not practically suitable for higher system of linear equations because they inherit inefficiency and instability of Cramer’s rule.