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Let A be in R^mxn, B in R^nxr, and C=AB. Show that:

(i) The column space of C is a subspace of the column space of A;

(ii) Rank(C) is smaller than or equal to min{rank(A), rank(B)}.

For (i) I tried to show that C can be written as linear combination of A but seems like I am missing something....

Please help!! Thanks

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# Column Spaces

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