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1bSet2 - all your answers 1 Problems 1-10 on page 13 This...

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CALIFORNIA INSTITUTE OF TECHNOLOGY Department of Mathematics Math 1b, Analytical; Homework Set 2 Due: Noon, Tuesday January 19, 2010 Read sections 1 through 5 and 9 through 16 of Chapter 2. Skip sections 6 and 7 of Chapter 2 as the discussion of inverses there is nonstandard. That is read pages 31 through 38 and 44 through 57. You can collaborate on the problems as long as you write up all solutions in your own words and understand those solutions. Remember to justify
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Unformatted text preview: all your answers. 1. Problems 1-10 on page 13. This time compute the dimension of S when S is a subspace, and prove your answer is correct. 2. Problem 22 on page 14 of Apostol. Do not appeal to Lemma 1D from class, as it was proved using this homework problem. 3. Problem 24 on page 14 of Apostol. In (d), exhibit a vector space V , a subspace S , and a basis for V which contains no basis for S . 1...
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