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Unformatted text preview: AMS 510.01 Fall 2007, Midterm #1 Name: Student ID: Score: /100 ( + /15 bonus) Attention: • Write all solutions on this paper; extra sheets are available if needed. • Explain your answers and show all work. For all problems except question 1 (true and false), correct answers with incomplete work will not be given full points. • Calculators may not be used. • All cellular phones must be turned off . Anyone with a phone that rings during the exam will be asked to turn in their exam and leave immediately. This includes textmessage alerts and phones in vibrate mode. 1. Indicate whether each of the following statements is true or false. n should be taken as any constant positive integer. (2 points each). (a) A system of linear equations may have exactly two solutions. (b) For any nonsingular matrices, A and B , if A 1 = B 1 , then A = B (c) The dot product of any two complex vectors is a real number, i.e. : ~u · ~v ∈ R , ∀ ~u, ~v ∈ C n (d) The set of all integers forms a field. (e) The vectors, { (1 , , 0) , (0 , 1 , 1) , (0 , 1 , 1) } form an orthonormal set....
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 Fall '08
 Feinberg,E
 Linear Algebra, Applied Mathematics, Matrices

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