Linear Algebra with Applications

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Math 20F - Linear Algebra Midterm Examination #1 - ANSWERS February 5, 2003 Write your name or initials on every page before beginning the exam. You have 50 minutes. There are six problems. You may not use notes, textbooks, or other materials during this exam. You must show your work in order to get credit. Good luck! Name: Student ID: Tuesday section time: I II III IV V VI Total
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Name: 2 The first problem asks you to circle all the correct answers. In each case, there are four possibilities (a)-(d). You should circle each of (a)-(d) that is a correct answer. This could be none of them, or one, or two, or three, or all four of them. I. For this problem, A , B and C are arbitrary, non-singular matrices. 1. ( ABC ) - 1 must be equal to which of the following? (a) C - 1 B - 1 A - 1 (b) ( BC ) - 1 A - 1 (c) ( C T B T A T ) - 1 (d) A - 1 B - 1 C - 1 ANSWERS: (a) and (b) 2. det( A T B ) must equal which of the following? (a) det( A )det( B ) (b) det( B ) det( A ) (c) det( A - 1 )det( B ) (d) det( B ) det( A - 1 ) ANSWERS: (a) and (d) 3. A - 1 AB must equal which of the following?
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