Quote from my textbook:
"The linear system Ax=b is consistent if and only if the number of nonzero rows of the augmented matrix [U| c], equals the number of nonzero rows in U."
[U,c] is the rref of [A,b]
The Attempt at a Solution
I understand "only if" but not "if". "Only if" is true since the elementary row operations do not affect the solutions to the system and it is clear that a linear combination of zeros cannot equal a nonzero number. Can someone help me with "if"?