## Consistency

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:

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