Question: 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

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 B; 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, B\" is an s X I matrix, B12 is an s X (r I) 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 )2 A1B1+A2B2. (b) (5 points) Prove that All A12 Bil B12 AllBil+ A12B21 AllB12 + A 12 B22 = A21 A 22 B21 B22 A21 BI1 + A22 B21 A21 B 12 + A 22 B 22 Hint: apply Part (a) followed by Question 4 from Tutorial 2

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