Linear Algebra with Applications

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ANSWER KEY Math 20F - Linear Algebra Midterm Examination #2 March 5, 2003 Instructor: Sam Buss, UC San Diego Write your name or initials on every page before beginning the exam. You have 50 minutes. There are seven problems. You may not use calculators, 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: 1 2 3 4 5 6 7 Total
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Name: 2 1. Write out the definitions of the following phrases (you may use other technical terms from the course without defining them). (a) A is a symmetric matrix.” ANSWER: A = A T . (b) A is an skew-symmetric matrix.” ANSWER: A = - A T . (c) v 1 , . . . , v n is a basis for V .” ANSWER: v 1 , . . . , v n are linearly independent and span V . (d) U and V are orthogonal ( U V ).” ANSWER: For every u U and every v V , u T v = 0 . (e) U is the orthogonal complement of V ( U = V ).” ANSWER: U = { u : for all v V , u T v = 0 } 2. Suppose A is an m × n matrix and that A has rank r .
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