# Thread: Row reduced echelon form and its meaning

1. ## Row reduced echelon form and its meaning

Hey.

I have the following question to solve:

* Given a matrix A that is size m x n and m>n.
Let R be the RREF that we get by Gaussian elimination of A.
Prove that the system equation Ax=0 has only one solution iff in every column of R there is a leading element.

I have some answer of intuition so I'm not really sure,
Let's assume that we had R with some free variable, and we know(?) that any free variable has a degree of freedom which means that it yields infinite number of solutions.

Now, I am not sure again about the establishment of this proof and to what extent it's accurate. Moreover, I am not if it proves the point of iff (equivalence).

Another similar question, but I have no idea what it means:

* Given a matrix A that is size m x n and m>n.
Let R be the RREF that we get by gaussian elimination of A.
Prove that for every $b \in \mathbb{R}^m$ the system equation Ax=b has a solution iff R doesn't have zero rows.

Thank you!

2. ## Re: Row reduced echelon form and its meaning

Rows of zeros