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## Homework Statement

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]

## Homework Equations

## 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"?