My Math Forum Row reduced echelon form and its meaning

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 November 17th, 2018, 08:54 AM #1 Newbie   Joined: Nov 2018 From: France Posts: 8 Thanks: 0 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!
 November 17th, 2018, 08:58 PM #2 Newbie   Joined: Nov 2018 From: France Posts: 8 Thanks: 0 Rows of zeros

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