math111_logo Row Echelon Form


Exercise List all the shapes of the row echelon forms of 2 by 2 matrices? What about the shapes of reduced row echelon forms? What about the other sizes (2 by 3, 3 by 2, etc.)?

Answer The following are all the shapes of 2 by 2 row echelon forms.

[ * # ]
0 *
[ * # ]
0 0
[ 0 * ]
0 0
[ 0 0 ]
0 0

The following are the corresponding 2 by 2 reduced row echelon forms.

[ 1 0 ]
0 1
[ 1 # ]
0 0
[ 0 1 ]
0 0
[ 0 0 ]
0 0