Row reduced echelon form: Prove that for every b in R^m, Ax=b has soln iff R has no 0

CStudent

New member
Joined
Nov 16, 2018
Messages
14
Hey.

* 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
gif.latex
the system equation Ax=b has a solution iff R doesn't have rows of zeros.

My attempt:
Maybe because b is supposed not to be equal to zero? And if we get some row of zeros we'll get that 0=b and it's a false proposition(?)
Not sure...

Thank you!
 
Top