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Midterm 1-Fall 2007

# Midterm 1-Fall 2007 - AMS 510.01 Fall 2007 Midterm#1 Name...

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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 text-message 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 non-singular 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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Midterm 1-Fall 2007 - AMS 510.01 Fall 2007 Midterm#1 Name...

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