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 and instability of Cramer's rule.

Modified Cramer’s Rule and its Application to Solve Linear Systems in WZ Factorization

“…then the unique solutions x = (x 1 , x 2 , ..., x n ) T , where B is the coefficient matrix of the system and c the column vector, to equation (1) can be obtained from an old method called Cramer's rule [1]. Cramer's rule has many drawbacks: fails when the coefficient matrix is singular, requires (n+1) determinants in its computation and has high computational time [2].…”