The [reduced row echelon form] rref(A) of a mxn matrix A is the end product 
of {Gauss-Jordan elimination}. The matrix rref(A) has the following 
properties:
  - if a row has nonzero entries, then the first nonzero entry is 1, 
    called {leading 1}.
  - if a columns contains a leading 1, then all other entries in that 
    column are 0. 
  - if a row contains a leading 1, then every row above contains a leading 
    1 further left. 
The algorithm to produce rref(A) from A is obtained by putting the cursor 
to the upper left corner and repeating the following steps until nothing 
changes anymore 
  1 if the cursor entry is zero swap the cursor row with the first row 
    below that has a nonzero entry in that column 
  2 divide the cursor row by the cursor entry to make the cursor entry = 1
  3 eliminate all other entris in cursor column by subtracting suitable 
    multiples of the cursorrow from the other row
  4 move the cursor down one row and and to the right one column. If the 
    cursor entry is zero and all entries below are zero, move the cursor 
    to the next column.
  5 repeat 4 if as long as necessary and move then to 1