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# hw10 - Week 10 1 Supplement Part A(2nd assignment 2 6.1 1st...

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Week 10: 1. Supplement, Part A (2nd assignment) 2. 6.1 1st order systems of DE 3. 6.2 Diagonalizable Homog Systems

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2 Recall that Part A of the supplement had an extended discussion of a 2-by-2 non-diagonalizale example – A.3, then A.5 and in final form in A.9. A second problem type, with the same 2-by-2 Jordan block J λ 1 , was described in Example A.17. These were the two cases of an eigenvalue of (algebraic) multiplicity 2, m 1 = 2, with an eigenspace of dimension 1 (geometric multiplicity 1, d 1 = 1 = m 1 = 2), from week 9. Recall that the Review sheet had an additional example, #31 . We have two new cases this week. These are covered in the supplement, Part A, Examples A18 and A19. Both cases have a single eigenvalue of multiplicity 3, one with an eigenspace of dimension 1 (and a single 3-by-3 Jordan block), the other with an eigenspace of dimension 2 (and so, two Jordan blocks, with the same diagonal entry – the eigenvalue – one 2-by-2,
the other 1-by-1. There was a review problem, #32 , with a single 3-by-3 block. We borrow another of

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