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Spring 2003 - Buss' Class - Exam 1

Spring 2003 - Buss' Class - Exam 1 - Math 20F Linear...

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Math 20F - Linear Algebra Midterm Examination #1 Spring, April 28, 2003 — Instructor: Sam Buss 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, calculators, or other materials during this exam. You must show your work in order to get credit. Good luck! Name: Student ID: Thursday section time: 1 2 3 4 5 6 Total
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Name: 2 1. Let A be an m × n matrix. a. State the definition of “the nullspace of A , N ( A )”. ANSWER: N ( A ) = { x : A x = 0 } . b. State the definition of “ A is skew-symmetric”. ANSWER: A = - A T . 2. Suppose that a 3 × 3 matrix A is row equavalent to 1 - 1 2 0 2 - 3 0 0 0 . (However, you do not know the matrix A itself.) For the following questions, either give an answer, or state “insufficient information” if you do not have enough information to answer the question. a. What is the value of det( A )? ANSWER: 0. b. Is A singular? ANSWER: Yes c. How many solutions does the equation A x = 0 have? ANSWER: Infinitely many.
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