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Unformatted text preview: ECE 580 / Math 587 SPRING 2011 Correspondence # 1 January 24, 2011 ASSIGNMENT 1 Reading Assignment: Text: Chapters 1 & 2. Recommended Reading: Curtain & Pritchard: Chapter 1. Problems (to be handed in): Due Date: Thursday, February 3 . 1. Let M and N be subspaces in a vector space. Show that [ M N ] = M + N , where the set operations [ ] and + are as defined in the text (also introduced in class). [This is Problem 3 on page 43 of the text.] 2. A convex combination of the vectors x 1 ,x 2 ,...,x n is a linear combination of the form x 1 + 2 x 2 + + n x n where i 0 for each i , and 1 + 2 + + n = 1. Given a set S in a vector space, let K be the set of vectors consisting of all convex combinations from S . Show that K = co(S), where co( ) is defined on p. 18 of the text. [This is Problem 4 on page 43 of the text.] 3. Obtain a continuous function x ( ) on the interval [ 1 , 1] which maximizes the integral 1- 1 t 3 x ( t )...
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