Question: 3. Let A1 be an m X S matrix, A; be an m X (n 5) matrix, B1 be an s X r matrix, and

3. Let A1 be an m X S matrix, A; 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 S matrix, A12 is an k X (n 3) matrix, A21 is an (m k) X S matrix, A22 is an (m k) X (n 5) matrix, B11 is an s X 1* matrix, B12 is an s X (r I) matrix, B21 is an (n s) X I matrix, B22 is an (n s) X (r I) matrix. B1 (a) (5 points) Prove that (Al A2 )( B 2 )2 A1B1+ A2132. 5. Suppose A is a 3 x 2 matrix and that R is the reduced row-echelon form of A. Suppose that A and R are related by the following sequence of elementary row-operations: R2- RI R24+ R3 R2-3R RI A R (a) (4 points) Write down the four elementary matrices corresponding to the four ele- mentary row operations displayed above.\f

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