sample_tt1_1

sample_tt1_1 - Math 136 Sample Term Test 1 NOTES Questions...

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Unformatted text preview: Math 136 Sample Term Test 1 NOTES: - Questions 4d, 5, 6 on this test cover material that will not be covered on our term test 1.- Students had 90 minutes to write this test, where you will have 110 minutes. 1. Short Answer Problems a) List the 3 elementary row operations. b) Does the spanning set span { (1 , 2 , 1) , (0 , 1 , 0) , (1 , , 1) } represent a line or a plane in R 3 ? Give a vector equation which describes it. c) What is the area of the parallelogram induced by ~a = (2 , 3) and ~ b = (1 ,- 1). d) If A is an n × m matrix and B is an m × p matrix, then what is the size of AB ? e) Explain why ~a × ( ~ b × ~ c ) must be a vector in the plane with vector equation ~x = s ~ b + t~ c , s,t ∈ R . 2. Consider the system of linear equations: z 1- z 2 + iz 3 = 2 i (1 + i ) z 1- iz 2 + iz 3 =- 2 + i (1- i ) z 1 + (- 1 + 2 i ) z 2 + (1 + 2 i ) z 3 = 3 + 2 i a) Row reduce the matrix to RREF using elementary row operations....
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This note was uploaded on 01/18/2011 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.

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sample_tt1_1 - Math 136 Sample Term Test 1 NOTES Questions...

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