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My question is really simple. I'm reading again Hoffman and Kunze's Linear Algebra book and I have the following doubt:

Let $A=(a_{ij})_{m\times n}$ be a row-reduced matrix with $r$ non-zero rows. Of course, we know that $r\le m$. My question is can we say that $r\le n$?

Thanks

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Rank of a matrix is equal to rank of its transpose. So, r is less than or equal to both m and n.

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