3. Let A1 be an m X 3 matrix, A2 be an m X (n 5) matrix, B1 be an s X r matrix, and B2 be an (n s) X r matrix. Also suppose that All is an k X 3 matrix, A12 is an k X (n 3) matrix, A21 is an (m k) X 3 matrix, A22 is an (m k) X (n 5) matrix, B11 is an s X 1* matrix, B12 is an s X (r 1*) matrix, B21 is an (n s) X 1* matrix, B22 is an (n s) X (r 1*) matrix. B] (a) (5 points) Prove that (Al A2 ) (B 2 )= AIBI + A2132. (b) (5 points) Prove that A11 A12) Bu B12): A11311+A12321 A11312+A12322) A21 A22 321 322 A21B11+A22B21 A21312+A22322 ' Hint: apply Part (21) followed by Question 4 from Tutorial 2