Question: Answer Question 2. (Strang 3.2.4849) Here you will prove that rank(AB) S min(rank(A), rank(B)). (a) Show that multiplication on the left by A can not

Answer Question

2. (Strang 3.2.4849) Here you will prove that rank(AB) S min(rank(A), rank(B)). (a) Show that multiplication on the left by A can not introduce new pivots columns into B; that is, if column j of B is a linear combination of the preceeding columns of B, the same column of AB is a linear combination of the preceeding columns of AB. Thus, rank(AB) g rank(B). (b) Prove that rank(BTAT) S rank(AT) (use the result of (a)). (c) Prove that rank(AB) S rank(A) (use the result of (b))

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