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My initial thought is no: when multiplying a matrix by another matrix or vector, the number of pivot points either stays the same or decreases. Does anybody have an example of when it increases after a transformation? Thank you.

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  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Dec 11, 2021 at 7:59
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    $\begingroup$ This immediately follows from the standard theorem about ranks of products: they cannot be higher than that of either factor. $\endgroup$ Dec 11, 2021 at 8:08

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