A system of linear equations is *consistent*
(that is, it has a solution, or general solutions)
if and only if an echelon matrix has *no* row of the form

with .

Thus, you should check for consistency as soon as an echelon form is obtained.
Then proceed the row reduction to produce a REF only when it is consistent.
EXAMPLE 4. Determine if the following system is consistent:

EXAMPLE 5, Determine the existence and uniqueness of the solutions to the following system:

Department of Mathematics