the second row which occurs in the third column. The first non-zero entry in the second row occurs in the third column and it occurs to the right of the first non-zero entry in the first row which occurs in the first column. So the matrix is in row-echelon form. The following matrices are not in row-echelon form: (i) (ii) Consider the matrix in (i).
In this matrix, the first non-zero entry in the third row occurs in the second column and it is on the left of the first non-zero entry in the second row which occurs in the third column. So the matrix is not in row-echelon form. Consider the matrix in (ii). In this matrix, the first non-zero entry in the second row occurs in the first column and it is on the left of the first non-zero entry in the first row which occurs in the second column.
So the matrix is not in row-echelon form. Method to reduce a matrix a ij m to a row-echelon form. Step Inspect the first row. If the first row is a zero row, then the row is interchanged with a non-zero row below the first row.
If a is not equal to , then go to step . Otherwise, interchange the first row R with any other row below the first row which has a non-zero element in the first column; if no row below the first row has non-zero entry in the first column, then consider a .If a is not equal to , then go to step . Otherwise, interchange the first row R with any other row below the first row which has a non-zero element in the second column; if no row below the first row has non-zero entry in the second column, then consider a .Proceed in the same way till we get a non-zero entry in the first row. This is called pivoting and the first non-zero element in the first row is called the pivot of the first row.