In our previous article, we discussed what the row echelon form of a matrix is. We learned that a matrix is said to be in the row echelon form if the following conditions hold:

1. The first non-zero element of a row is to the right of the first non-zero elements of the rows above.
2. Rows that contain all zeros are at the bottom of all rows that contain at least one non-zero element.

For example, the matrices given below are in the row echelon form.

We also discussed what pivots of a row echelon form of a matrix are. We learned that when a matrix is in the row echelon form, the left-most non-zero element of each row is called a pivot. For example, for the given matrix A, 1 and 5 are the pivots.

After finding out the row echelon form of a matrix, we can perform some row reduction. For example, we can divide each row with the pivot of the row so that the pivot becomes a 1. In that way, we can perform row reduction for each row and make the pivot of each row a 1. After such transformation, the row echelon form of the matrix will be called the reduced row echelon form of the matrix.

So, the matrix A here is in the reduced row echelon form.

So, matrices given below are in the row reduced echelon form.

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