math111_logo Existence


Exercise List all shapes of the row echelon forms the the augmented matrices of consistent systems of 2 equations and 2 variables. What about systems of other sizes?

Answer For 2 equations in 2 variables, we look for all 2 by 3 matrices with no rows of the form [0 0 ≠0]. The following are all such shapes.

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