Linear Algebra 11L5: The Column Space of AB

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Didn't really get the relevance of the first part to the problem at hand. Why Does Dr. Grinfeld show that there is no B that satisfies AB=C, when the title declares we wish to investigate the column space of C when such a relation (AB=C) does exist?

kottelkannim
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Couldn't it be proved from the fact
dim col.space C + dim ker C = # cols C
?.. Intuition says, these facts are somehow related.

ekaptsv