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Unformatted text preview: 1 THE UNIVERSITY OF WESTERN ONTARIO Department of Applied Mathematics London Ontario Applied Mathematics 025b Second Tutorial Test – February 21, 2008 60 min Name: Solution Section 2 Closed book. Only simple calculators are allowed. 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. Instructor – Dr. N. Kiriushcheva PART A. Mark the correct answer.  1.1. Given two rectangular matrices A and B , (a) it is always true that AB = BA ; (b) it is never true that AB = BA ; (c) it is only true that AB = BA when A and B are square matrices; (d) it is sometimes true that AB = BA , but not always; (e) in the special case that A and B are nonsingular, then it is true that AB = BA . Answer: d  1.2. True-False Questions: (a) The product of two elementary matrices is an elementary matrix. True False (b) If A is a singular n × n matrix, then the reduced row-echelon form of A has at least one row of zeros. True False (c) A × adj( A ) is a diagonal matrix only if A is a diagonal matrix. True False (d) For any n × n matrix det( I + A ) = 1 + det( A ). True False Answer: (a) : False (b) : True (c) : False (d) : False AM 025b Test 2 – February 21, 2008 2 Student #: FOR INSTRUCTOR’S USE ONLY 1 2 3 4 5 6 7 Total 4 8 8 10 10 10 10 60  2.1. Suppose that A is 4 × 5, B is 4 × 5, C is 5 × 2, D is 4 × 2, E...
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