Problem 2: (15 points) a) Let A, B and C be 3 matrices such that the product ABC is 3 x 4. What do you know about the sizes of A, B and C? Explain. 1 2 b) The product MNis | 4 1 | and M' and N' are matrices of the same sizes as M and N respectively. -1 3 If row 2 of M'= 2 x row 2 of M and column 1 of N'= 3 x column 1 of N, what do you know about the product M'N'? Explain. ) Give an example of a matrix D with Nul(D) = Span((1,1,1)). Explain. d) Give an example of a matrix E such that the system Ex = b is consistent if and only if b in Span((1, 2)) and the reduced echelon form of F is [ 0 1 g ] . Explain. 0 0 e) Can you build a matrix F such that F' has rank 2 and {(1,0,1),(1,1,1)} is a basis for Nul(F)? Explain