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Unformatted text preview: Math 136 Assignment 4 Solutions 1. Let A = 1 0 1 2 1 2 , B = 3 2 1 0 1 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 9 d) B T C = 4 1 8 e) C T C = 9 . f) BA T = 4 10 1 2 1 2. If AB is a 2 × 4 matrix, then what size are the matrices A and B ? Solution: Since AB is 2 × 4, A must have 2 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 2 × n and B is n × 4. 1 2 3. Determine which of the following sets are linearly independent. a) S = { (1 , 2 , 1 , 1) , (2 , 3 , 3 , 4) , (3 , 6 , 4 , 5) } . Solution: Consider (0 , , , 0) = c 1 (1 , 2 , 1 , 1) + c 2 (2 , 3 , 3 , 4) + c 3 (3 , 6 , 4 , 5) = ( c 1 + 2 c 2 + 3 c 3 , 2 c 1 3 c 2 6 c 3 , c 1 + 3 c 2 + 4 c 3 , c 1 + 4 c 2 + 5 c 3 ) This is the homogeneous system of linear equations with coefficient matrix...
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This note was uploaded on 05/04/2010 for the course MATH 136 taught by Professor All during the Spring '08 term at Waterloo.
 Spring '08
 All
 Math, Linear Algebra, Algebra

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