math136 - Math 136 Assignment 1 Solutions 1. Compute each...

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Assignment 1 Solutions 1. Compute each of the following. a) 2 - 3 5 - 1 - 3 - 2 Solution: 2 - 3 5 - 1 - 3 - 2 = 1 0 7 b) - 2 1 2 3 - 2 3 0 - 1 Solution: - 2 1 2 3 - 2 3 0 - 1 = - 8 - 4 - 4 2. For each of the following sets: i) Determine if the set is linearly dependent or linearly independent. Justify. ii) Describe geometrically the span of the set and give a simplified vector equation which describes it. a) B 1 = 2 1 0 , 0 0 0 . Solution: i) Since the set contains the zero vector it is linearly dependent. ii) The span of the set is ~x = s 2 1 0 + t 0 0 0 = s 2 1 0 . Hence, the span of the set is the line in R 3 with vector equation ~x = s 2 1 0 , s R . b) B 2 = 1 1 1 , - 2 - 2 - 2 , 3 3 3 Solution: i) We have 2 1 1 1 + - 2 - 2 - 2 +0 3 3 3 = 0 0 0 . Hence, by definition, the set is linearly dependent. 1
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This note was uploaded on 11/25/2010 for the course MATH 136 taught by Professor All during the Spring '08 term at Waterloo.

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math136 - Math 136 Assignment 1 Solutions 1. Compute each...

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