A matrix is said to be in Reduced-Row-Echelon-Form if
the following conditions are satisfied:
If all the properties, defined above, except the last are satisfied then
we say that the matrix is in Row-Echelon-Form. Sometimes
even if the matrix satisfies only properties 2 and 3
and not 1 and 4 we say that it is in row echelon
- The first nonzero number in a row is a 1. (We call it a leading 1).
- All rows of zeros (if there are any) are together at the bottom of the matrix.
- Each column that contains a leading 1, has only zeros below it.
- Each column that contains a leading 1 has zeros everywhere else.
The idea here is that once the matrix is in one of these forms, the system of equations
that has this as its augmented matrix can be solved with little or almost no effort.