Question: Problem 5 Problem 5 Let A and B be matrices such that AB is defined. i) Prove that ker(B) C ker(AB). Prove that im(AB) C

Problem 5

Problem 5 Let A and B be matrices such that AB is defined. i) Prove that ker(B) C ker(AB). Prove that im(AB) C im( A). ii) Prove that if im(B) C ker( A), then AB is the zero matrix. iii) Suppose ker(A) = {0} and ker(B) = {0}. Find ker ( AB)

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