The following are the properties of a matrix in the reduced row-echelon form:
1. Each row contains only zeros until the first nonzero element, which must be 1. For example:
2. As the rows are followed from top to bottom, the first nonzero number occurs further to the right than in the previous row. For example:
3. The entries above and below the first 1 in each row must all be 0. For example:
According to the above, the augmented matrix that is in reduced form row echelon form is the shown in option B because it is the only matrix that satisfies the mentioned properties.
