Proving Consistency of Ax=b: A Fundamental Property of Matrices

[DotKite]

Homework Statement

Let A be mxn prove Ax=b is consistent for all b if and only if rank(A) = m

Homework Equations

See above

The Attempt at a Solution

I do not know where to begin on this. Any hints would be great

 

[rock.freak667]

What does it mean for a system to be consistent?

If you augment matrix A and b to get [A|b] and you row reduce, how many rows of non-zeros would you need to get a consistent solution?