Full rank decomposition, where matrix come from?

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While studying full rank decomposition, I found the following:

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I understand it until $C$. Where does $C$ comes from?

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The rows of matrix $C$ are just a basis for rows of matrix $A$.

The rows of matrix $B$ are the combination coefficient such that $BC=A$.

Indeed the left multiplication $BC$ correspond to a row combination of the rows of $C$.