{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Week 10: 1. Supplement, Part A (2nd assignment) 2. 6.1 1st order systems of DE 3. 6.2 Diagonalizable Homog Systems
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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,
Image of page 2
the other 1-by-1. There was a review problem, #32 , with a single 3-by-3 block. We borrow another of
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern