Linear Algebra 17 | Properties of the Matrix Product

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This is my video series about Linear Algebra. I hope that it will help everyone who wants to learn about it.

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(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
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In the proof you can swith the sums and applied distributive law because is a finite sum. Is that correct? If we have an infinite matrix we would need more assumptions?

MrWater