MATLAB Cramer’s Code for Solving Linear System of Equations

This code solves a system of n equations and variables using Cramer’s Method, where you need just to insert your Coefficients Matrix A and Right Hand-Side Matrix B, the code will do everything since then. The results is the Roots of the given system.

Cramer’s rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one column by the column vector of right-hand-sides of the equations.

The General Case:

Consider a system of n linear equations for n unknowns, represented in matrix multiplication form as follows:

where the n × n matrix A has a nonzero determinant, and the vector x = (x1, …, xn)^T is the column vector of the variables. Then the theorem states that in this case the system has a unique solution, whose individual values for the unknowns are given by: