Consider linear equations in unknowns namely of as:
Associated with this system of equations is the matrix:
Consider the matrix
We can apply elementary row operations in the matrix A to get the matrix in reduced form.
An elementary row operation on the given matrix A is an algebraic manipulation of the matrix that corresponds to one of the following:
1. Interchanging any two rows such as the and the rows of the matrix A;
2. Multiplying one of its rows such as the row by a real number where ;
3. Adding one of its rows such as the row to the times row.