Originally Posted by

**dannyboycurtis** I have to prove the following statement, or provide a counterexample:

**If the coefficient matrix of a system of ***m* linear equations in* n* unknowns has rank *m*, then the system has a solution.

My thought is that this statement is true, and I think the proof would use the following theorem:

Let Ax=b be a system of linear equations. Then the system is consistent (the solution set is nonempty) if and only if rank(A) = rank(A|b).

Is it true that if an mxn matrix has rank m as assumed that the rank of the corresponding augmented matrix (A|b) would ALWAYS have the same rank?