Gauss-Jordan Elimination MethodThe followingrow operationson the augmented matrix of a system produce the augmented matrixof an equivalent system, i.e., a system with the same solution as the original one.•Interchange any two rows.•Multiply each element of a row by a nonzero constant.•Replace a row by the sum of itself and a constant multiple of another row of the matrix.For these row operations, we will use the following notations.•Ri↔Rjmeans: Interchange rowiand rowj.•αRimeans: Replace rowiwithαtimes rowi.•Ri+αRjmeans: Replace rowiwith the sum of rowiandαtimes rowj.The Gauss-Jordan elimination method to solve a system of linear equations is described in thefollowing steps.1. Write the augmented matrix of the system.2. Use row operations to transform the augmented matrix in the form described below, which iscalled thereduced row echelon form(RREF).(a) The rows (if any) consisting entirely of zeros are grouped together at the bottom of thematrix.(b) In each row that does not consist entirely of zeros, the leftmost nonzero element is a 1(called a leading 1 or a pivot).(c) Each column that contains a leading 1 has zeros in all other entries.(d) The leading 1 in any row is to the left of any leading 1’s in the rows below it.3. Stop process in step 2 if you obtain a row whose elements are all zeros except the last one onthe right. In that case, the system is inconsistent and has no solutions. Otherwise, finish step2 and read the solutions of the system from the final matrix.