wa1 - problem to be it may take two If you have written...

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Winter 2011 Math 67 Linear Algebra Writting Assignment 1 Instructions. The purpose of this assignment is less mathematical and more to familiarize you with writing mathematics well. As such, you are to type a solution to the following problem, pretending that your exposition will appear as an example in a textbook. The point is to include just the right amount of detail: Too much detail is bad, while too little is worse. Your solution will probably fit on a single typed page, but depending on your writing style or how difficult you find the
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Unformatted text preview: problem to be, it may take two. If you have written three pages, you have included too much. If you have less than 1 / 2 of a page you have probably included too little. Exercise. Let V = C n and 1 be the all ones vector 1 = e 1 + ··· + e n . Let W be the subspace of V spanned by those vectors of the form λ 1 e 1 + λ 2 e 2 + ··· + λ n e n such that λ 1 + λ 2 + ··· + λ n = 0 ∈ C . Prove that there is a direct sum decomposition V = ( C · 1 ) ⊕ W, as complex vector spaces. What is a basis for W ? 1...
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This note was uploaded on 11/13/2011 for the course MATH 67 taught by Professor Schilling during the Winter '07 term at UC Davis.

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