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ECON 3410 Mathematical Economics Assignment 3 1. Given A = (6 9). B = (3 -2). and c = (8 3). find: (a) A + B (b) C - A (c) 3A (d) 4B + 2C 2. Given A (3 0). B = (3 8). and C =(6 3): (a) Is AB defined? Calculate AB. Can you calculate BA? Why? (b) Is BC defined? Calculate BC. Is CB defined? If so, calculate CB. Is it true that BC= CB? 3. Find the product matrices in the following (in each case, append beneath every matrix a dimension indicator): ( d) (a b c ) (0 2 ) (a) (A + B) + C = A+(B + C) ( b) (A + B) - C = A+(B - C) 5. Given A = (01 52 7 ). b = (6). and x = (x;): (a) Calculate: i. Al ii. IA iii. Ix iv. x'l Indicate the dimension of the identity matrix used in each case. (b) Calculate: i. Ab ii. Alb iii. x'IA iv. x'A Does the insertion of /in ii. affect the result in i.? Does the deletion of /in iv. affect the result in iii.? (c) What is the dimension of the null matrix resulting from each of the following? (Note: If the null matrix is O, then premultiply means multiply Obefore A, that is, OA. Postmultiply means multiply Oafter A, that is, AO.) i. Premultiply A by a 5 x 2 null matrix. ii. Postmultiply A by a 3 x 6 null matrix. iii. Premultiply bby a 2 x 3 null matrix. iv. Postmultiply x by a 1 x 5 null matrix. 6. Given A = (-1 3). B = (8 7). and C = (6 ; ;). find A', B', C