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Unformatted text preview: M ATH 223 P ROBLEM S ET 5 D UE : 11 October 2007 When you hand in this problem set, please indicate on the top of the front page how much time it took you to complete. Reading. 1.61.8. Problems from the book: the starred problems will be graded. 1.6.2, 1.6.3, 1.6.6 , 1.6.8. 1.7.1, 1.7.2, 1.7.4, 1.7.6, 1.7.10 , 1.7.11, 1.7.17, 1.7.18 Additional problems: 1. Give an example of a sequence in R that has the properties that, first, for every natural number k N, there is a subsequence converging to k; and second, for any convergent subsequence, the limit is a natural number. 2. Find all solutions to z2 + (3 + 3i)z  (2 + 6i). 3. Let f : M22(R) M22(R) be the function defined by f(A) = A AT , the product of the matrix with its transpose. What is the directional derivative of f at the point 2 1 a b B= in the direction of  = v ? Is the directional derivative at B 3 5 c d linear as a function of  ? v ...
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This homework help was uploaded on 02/24/2008 for the course MATH 2230 taught by Professor Holm during the Fall '07 term at Cornell University (Engineering School).
 Fall '07
 HOLM

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