Reduced row echelon form is a special form of a matrix where all the leading coefficients are 1 and all the other entries in the same column are 0. It is also known as row canonical form or reduced row-echelon matrix.
Reduced row echelon form is important because it allows us to easily solve systems of linear equations and to find the inverse of a matrix.
The reduced row echelon form of a matrix can be found by using elementary row operations such as multiplying a row by a non-zero scalar, swapping two rows, or adding a multiple of one row to another row.
In row echelon form, the leading coefficient of each row is 1, but there are no restrictions on the other entries in the same column. In reduced row echelon form, all the other entries in the same column must be 0.
Not every matrix can be reduced to reduced row echelon form. A matrix is only reducible if it is a square matrix or has more rows than columns. Additionally, it may not be possible to reduce a matrix if there are no leading coefficients in a column or if there are infinitely many solutions to the system of equations represented by the matrix.