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527ass8

# 527ass8 - hint given with this it can be done by inspection...

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642:527 ASSIGNMENT 8 FALL 2009 Turn in starred problems Tuesday 11/03/2009. Section 9.9: 4 (a), (e)* Section 9.10: 2 (a), (c)*; 3 Section 17.2: 5 (a), (e), (g); 12 (a), (e), (j)*, (s) Section 17.3: 1, 4 (a), (c)*, (l)* 8.A* Exercise 1 from the notes on Expansions in Orthogonal Bases, available on the web page. Comments: (a) For the problems in Section 19.10: the best approximation to a given vector within the “span” of some vectors { e 1 , e 2 ,... } means the best approximation as a linear combination of those vectors. (b) 17.2 12(j) is a bit tricky—think carefully. On the other hand, 17.3 4(l) is easy, if you use the hint given: with this it can be done by inspection. The two problems are related.
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Unformatted text preview: hint given: with this it can be done by inspection. The two problems are related. (c) The extra exercise 8.A involves the evaluation of many integrals; these are simple (just poly-nomials) but it is still a nuisance. You are welcome to use Maple, Mathematica, or some other program to do these. If you do so, write the integral out out explicitly before giving the answer. For example, for part (a) you might write a f, g A = i 2 f ( x ) g ( x ) dx = i 2 (1 − x ) dx = 0; a g, g A = i 2 g ( x ) 2 dx = i 2 (1 − x ) 2 dx = 2 3 , so b g b = r a g, g A = R 2 3 ....
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