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Unformatted text preview: , the set of all subsets of X , has 2 n elements. Hint: use induction. Part II 4. Suppose X,Y,Z are Fnite-dimensional vector spaces over R with bases U,V,W re-spectively, S L ( X,Y ) and T L ( Y,Z ). Summarize the relationships among S , T , T S , and their matrix representations using a commutative diagram. 1 Explain the interpretation of the diagram. 5. Consider the metric space ( X,d ), where X = Q [ , 1 ], Q is the set of all rational numbers, and d is the usual Euclidean metric d ( x,y ) = | x y | . Show that ( X,d ) is not compact by exhibiting an open cover of X that has no Fnite subcover. 1 If you dont remember the commutative diagram given in class and the handout, dont panic. Think through the relationships and explain them, if possible with a diagram. 1...
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This note was uploaded on 08/01/2008 for the course ECON 204 taught by Professor Anderson during the Fall '08 term at University of California, Berkeley.
- Fall '08