Question: 3. [2 points each] (a) If A is an m X n matrix, What are the possible values of nullity of A? (b) If A

3. [2 points each] (a) If A is an m X n matrix, What are the possible values of nullity of A? (b) If A is an m X n matrix and let B be the RREF of A. Show by example that 001(A) 7E col(B). 4. [2 points each] (a) Let A be an m x n matrix. Prove that A'A is an n x n matrix with rank(AT A) = rank(A). (b) Prove that the square matrix A'A is invertible if and only if rank(A) = n

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3. [2 points each] (a) If A is an m x n matrix, what are the possible values of nullity of A? (b) If A is an m x n matrix and let B be the RREF of A. Show by example that col(A) # col(B)

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