problems-9-223-F07 - M ATH 223 Reading 3.53.7 P ROBLEM S ET...

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Unformatted text preview: M ATH 223 Reading. 3.53.7. P ROBLEM S ET 9 D UE : 13 November 2007 Problems from the book: the starred problems may be carefully graded. You will be given a "completeness" score, depending on how carefully you complete these problems. 3.3: 5, 6 , 9, 13 3.4: 8, 11 3.5: 15, 17, 14 3.6: 6 Additional problems: These will be carefully graded! 1. Suppose V and W are vector spaces over R. Show that the set of linear transformations L(V, W) = {T : V W | T is linear}, is itself a vector space over R. 2. Suppose that f : R2 R satisfies Laplace's equation D2f + D2f = 0. True or false: 1 2 the function x x 2 2 g = f x +y y y x2 +y2 also satisfies Laplace's equation. Prove this, or give a counterexample. ...
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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.

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