Matrix Method for solving systems of equations is also known as Row Echelon Method. The matrix method is similar to the method of Elimination as but is a lot cleaner than the elimination method.Solving systems of equations by Matrix Method involves expressing the system of equations in form of a matrix and then reducing that matrix into what is known as Row Echelon Form.Below are two examples of matrices in Row Echelon FormThe first is a 2 x 2 matrix in Row Echelon form and the latter is a 3 x 3 matrix in Row Echelon form.