Cullen in a question seems to say this;(adsbygoogle = window.adsbygoogle || []).push({});

You have a matrix A of any size. Make a matrix B consisting of only the linearly independent columns of A, choosing them by going from left to right through the columns of A. Then make a matrix C such that BC=A [The q was to prove this is always possible. But I'm not asking about that]

He then says that the rows of C are exactly the rows of A in row reduced echelon form. I tried an example, and it works.

My q is, why is this so? I assume it's not just coincidence, so what is going on?

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# Why does this work?

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