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# Lab 11 - where<f g> = âˆ f(x g(x dx show that the...

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MATH 342-010 Differential Equations with Linear Algebra II Fall 2009 Due November 23, 2009 Homework 11 Leon Section 5.4 1. Page 252, number 2 2. Page 254, number 17 3. Page 254, number 29 4. Which of the following are inner product spaces? (a) R n where <X, Y> = -X T Y; (b) R n where <X, Y> = 2X T Y; 1 (c) C[0, 1] where <f, g> = (f(x) + g(x)) dx 0 5. Consider the inner product space[0,

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Unformatted text preview: ] where <f, g> = âˆ« f(x) g(x) dx, show that the functions 1/âˆš , (2/âˆš ) cos mx 0 m =1, 2, â€¦â€¦ form a set of mutually orthogonal vectors. Section 5.5 6. Page 270, number 1 7. Show that the set B is an orthonormal basis in R 3 B = 8. Page 271, number 7 9. Page 272, number 12 10. Page 273, number 27 parts (a) and (b)...
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