assign4_soln - Math 136 Assignment 4 Solutions 3 2 1 2 1 0...

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Math 136 Assignment 4 Solutions 1. Let A = 1 0 - 1 2 1 - 2 , B = 3 2 - 1 0 1 0 1 3 3 , C = - 2 1 2 . Determine the following products or state that they are undefined. Solution: a) AB = 2 - 1 - 4 4 - 1 - 8 . b) BA is undefined since B has 3 columns but A has only 2 rows. c) AC = - 4 - 7 d) B T C = - 4 3 8 e) C T C = 9 . f) BA T = 4 10 0 1 - 2 - 1 2. If AB is a 3 × 4 matrix, then what size are the matrices A and B ? Solution: Since AB is 3 × 4, A must have 3 rows and B must have 4 columns and the number of columns of A must equal the number of rows of B . Hence A is 3 × n and B is n × 4. 3. Determine which of the following sets are linearly independent. a) S = 1 - 2 1 1 , 2 - 3 2 3 , 3 - 7 3 2 . Solution: Consider 0 0 0 0 = c 1 1 - 2 1 1 + c 2 2 - 3 2 3 + c 3 3 - 7 3 2 = c 1 + 2 c 2 + 3 c 3 - 2 c 1 - 3 c 2 - 7 c 3 c 1 + 2 c 2 + 3 c 3 c 1 + 3 c 2 + 2 c 3 1
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