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Unformatted text preview: 1 THE UNIVERSITY OF WESTERN ONTARIO Department of Applied Mathematics London Ontario Applied Mathematics 025b Midterm Examination – March 7, 2008 7:00 p.m. - 9:30 p.m. (2 hours 30 min) Name: Solution The exam is open book. Print your name above and student number on the page 2. Justify answers by showing sufficient work to get the full marks. Solve each problem in space provided for that specific problem. Use margins or back of each sheet to do your rough work. Circle your (lecture) section 01 – Z. Krougly 02 – N. Kiriushcheva PART A. Mark the correct answer.  1. True-False Questions: (a) Suppose A and B are n × n matrices and A is nonsingular, then if AB = AC , then B = C True False (b) If A is nonsingular, then ( A T )- 1 = ( A- 1 ) T True False (c) A linear system can have exactly two solutions. True False (d) A linear system of two equations in three unknowns cannot have ex- actly one solution. True False (e) Any n × n system of linear equations can be solved using Cramer’s rule. True False (f) A set of vectors v 1 , v 2 , ..., v r is linearly dependent if the equation k 1 v 1 + k 2 v 2 , . . . k r v r = has a nontrivial solution True False Answer: (a) True , (b) True , (c) False , (d) True , (e) False , (f) True AM 025b Midterm Examination – March 7, 2008 2 Student #: FOR INSTRUCTOR’S USE ONLY 1 2 3 4 5 6 7 Total 6 10 24 16 24 10 10 100 PART B. Show all steps of your calculations....
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- Spring '11
- Linear Algebra, Midterm Examination, Det