assign1_soln

assign1_soln - Math 136 Assignment 1 Solutions 1. Compute...

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Assignment 1 Solutions 1. Compute each of the following. a) Solution: 1 3 4 + - 1 1 2 = 0 4 6 . b) Solution: 3 - 1 1 - 2 - 2 2 0 3 = - 7 3 - 12 . 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 = 1 1 - 3 , - 1 - 1 3 . Solution: i) Since ( - 1) 1 1 - 3 + - 1 - 1 3 = 0 0 0 , the set is linearly dependent. ii) The second vector is a scalar multiple of the first, so the simplified vector equation is ~x = t 1 1 - 3 , t R . The span of the set is a line in R 3 that passes through the origin. b) B 2 = 1 2 1 , - 2 - 4 - 2 , 2 1 2 . Solution: i) Since 2 1 2 1 + - 2 - 4 - 2 + 0 2 1 2 = 0 0 0 , the set is linearly dependent. ii) The second vector is a scalar multiple of the first, so we get that the simplified vector equation is ~x = c 1 1 2 1 + c 2 2 1 2 , c 1 , c 2 R . The span of the set is a plane in R 3 which passes through the origin. 1
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This note was uploaded on 09/19/2011 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.

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assign1_soln - Math 136 Assignment 1 Solutions 1. Compute...

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