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mat1302-practice-midterm3-solutions

mat1302-practice-midterm3-solutions - MATH 1302 PRACTICE...

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MATH 1302 - PRACTICE THIRD MIDTERM EXAM SOLUTIONS WINTER 2008 1. Suppose an economy consists of three sectors – manufacturing, agriculture and services – with unit consumptions as given in the following table. Purchased Inputs Consumed per Unit of Output From: Manufacturing Agriculture Services Manufacturing .20 .20 0 Agriculture .30 .10 .30 Services .10 0 .20 What production levels are needed to satisfy a final demand of 40 units from manufac- turing, 60 units from agriculture, and 80 units from services? Answer: We have C = . 2 . 2 0 . 3 . 1 . 3 . 1 0 . 2 , I - C = . 8 - 2 . 0 - . 3 . 9 - . 3 - . 1 0 . 8 , d = 40 60 80 . We row reduce £ I - C d / to get . 8 - . 2 0 40 - . 3 . 9 - . 3 60 - . 1 0 . 8 80 1 0 0 82 . 8 0 1 0 131 . 0 0 0 1 110 . 3 . Therefore, to meet the given demand, manufacturing needs to produce 82.8 units, agriculture needs to produce 131.0 units and services needs to produce 110.3 units. 2. Suppose that z = - 1 + 4 i, w = 2 - 2 i. Perform the following operations, writing your answers in the form a + bi where a, b R . a) | z | Solution: | z | = p ( - 1) 2 + 4 2 = 17. b) ¯ w Solution: ¯ w = 2 + 2 i . c) w/z Solution: w z = 2 - 2 i - 1 + 4 i · - 1 - 4 i - 1 - 4 i = - 10 - 6 i 17 = - 10 17 - 6 17 i.
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2 MAT 1302 - PRACTICE THIRD MIDTERM EXAM SOLUTIONS d) wz Solution: wz = (2 - 2 i )( - 1 + 4 i ) = 6 + 10 i e) 3 z + 2 w Solution: 3 z + 2 w = 1 + 8 i 3. If A =
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