How to prove rank a+b <= rank a + rank b?
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Prove that rank(AB) ≤ rank(A), and hence, rank(AB) ≤ min {rank(A), rank(B)}. To multiply A by B on the right means that every column of the result AB is a linear combi- nation of the columns of A. Using the above definition for the rank of a matrix we get the desired result, that rank(AB) ≤ rank(B).
Prove that rank(AB) ≤ rank(A), and hence, rank(AB) ≤ min {rank(A), rank(B)}. To multiply A by B on the right means that every column of the result AB is a linear combi- nation of the columns of A. Using the above definition for the rank of a matrix we get the desired result, that rank(AB) ≤ rank(B).
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Answer: its a identity
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