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Midterm 1-Fall 2008 - AMS 510.01 Fall 2008 Midterm#1 Name...

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AMS 510.01 Fall 2008, 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.
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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) The set of all rational numbers is closed with respect to both addition and multiplication. (b) The dimension of the vector space of all vectors of the form ( a, b, 0) is three. That is: V = { x : x = ( a, b, 0) , a, b R } → dim( V ) = 3 (c) 1 0 0 0 0 0 2 0 0 0 0 1 0 3 0 0 = 3 (d) The set of all matrices of the form: a 0 0 b where a, b C , forms a vector space.
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