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# hw8 - 11 Let the numbers S n be the determinants dened in...

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Math 215 HW #8 Due 5:00 PM Thursday, April 1 Reading: Sections 4.1–4.3 from Strang’s Linear Algebra and its Applications , 4 th edition. Problems: Please follow the guidelines for collaboration detailed in the course syllabus. 1. Problem 4.2.4. 2. Problem 4.2.6. 3. Problem 4.2.8. 4. Problem 4.2.10. 5. Problem 4.2.14. 6. Problem 4.2.26. a ij is the entry in the i th row and j th column of the matrix A . 7. Problem 4.3.6. 8. Problem 4.3.8. 9. Problem 4.3.14. Feel free to use whatever technique for computing the determinant you prefer. 10. Problem 4.3.28.
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Unformatted text preview: 11. Let the numbers S n be the determinants dened in Problem 4.3.31. (a) For any n &amp;gt; 2 prove that S n = 3 S n-1-S n-2 . (b) For any k let F k denote the k th Fibonacci number (recall that the Fibonacci sequence 1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , 55 , 89 , 144 , . . . is dened by F k = F k-1 + F k-2 ). Prove that F 2 n +2 = 3 F 2 n-F 2 n-2 . (c) Show that S n = F 2 n +2 for each n . 12. ( Bonus Problem ) Problem 3.5.12. Youll need to read Section 3.5 to do this problem. 1...
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