LinAlg Test 1 [Sample from 05]

# LinAlg Test 1 [Sample from 05] - The University of Western...

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Unformatted text preview: The University of Western Ontario Applied Mathematics 025 First Tutorial Test: Sample from 2005 Note that the material covered on the test will vary from semester to semester Time: 60 minutes Use the scantron sheet to answer questions in part A. Use this examination book to answer questions in part B. Part A is worth 50% of the test marks; Part B is worth 50%. You are allowed to use calculators and your textbook during this test. Name: STUDENT NUMBER 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 PART A: USE SCANTRON FOR SOLUTIONS 1. Have you filled in your student number on the scantron sheet? (a) Yes, I have filled it in and checked it. (b) Yes, I filled it in; maybe I’ll check it later. (c) No, I’ll do it later, I promise. (d) No, I do not care whether I get credit for this test. (e) No, I expect you guys to read my mind Answer: a 2. The system of equations xa + 5 b + 3 c = 4 y xa 2 + 2 b − 5 c = 3 z 3 a + b + c = − xy (a) is linear in { x, y, z } but nonlinear { b, c } (b) is linear in { x, y } and { b, c } (c) is nonlinear in { x, y } but linear { a, b } (d) is linear in { y, z } but nonlinear { a, b, c } (e) is linear in { x, y, z } and linear in { a, b, c } Answer: d 3. Consider a junction in a network of pipes carrying water, as illustrated. a63 a54 a45 a27 20 i 3 i 1 i 2 By applying the conservation of mass to this junction, we conclude the following. (a) All the arrows point towards the central point, so there is no way for the water to escape. Therefore the equations will have no solution. (b) − 20 + i 3 + i 1 − i 2 = 0. (c) +20 − i 3 + i 1 + i 2 = 0. (d) +20 + i 3 + i 1 + i 2 = 0. (e) None of the above. Answer: d. 4. The coefficients of a polynomial of degree 6 have to be calculated from data points. (a) It is always possible to find the coefficients, given 7 distinct data points....
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LinAlg Test 1 [Sample from 05] - The University of Western...

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