sample_tt1_1_ans

sample_tt1_1_ans - Math 136 Term Test 1 Answers NOTE: -...

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Math 136 Term Test 1 Answers NOTE : - Only answers are provided here (and some proofs). On the test you must provide full and complete solutions to receive full marks. 1. Short Answer Problems a) List the 3 elementary row operations. Solution: 1. Multiply a row by a non-zero constant 2. Swap two rows 3. Add a multiple of one row to another. b) Does the spanning set span { (1 , 2 , 1) , (0 , 1 , 0) , (1 , 0 , 1) } represent a line or a plane in R 3 ? Give a vector equation which describes it. Solution: This is a plane with vector equation ~x = t (1 , 0 , 1) + s (0 , 1 , 0) . c) What is the area of the parallelogram induced by ~a = (2 , 3) and ~ b = (1 , - 1). Solution: The area is ± ± ± ± det ² 2 3 1 - 1 ³± ± ± ± = | 2( - 1) - 3(1) | = | - 5 | = 5. d) If A is an n × m matrix and B is an m × p matrix, then what is the size of AB ?. Solution: AB is n × p . e) Explain why ~a × ( ~ b × ~ c ) must be a vector in the plane with vector equation ~x = s ~ b + t~ c , s,t R . Solution: Suppose that ~n = ~ b × ~ c 6 = ~ 0. Then ~n is orthogonal to both ~ b and ~ c , so it is a normal vector to the plane through the origin that contain ~ b and ~ c
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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_ans - Math 136 Term Test 1 Answers NOTE: -...

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