{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ws10 - Math 464 Worksheet 10 The goal in this worksheet is...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 464, Worksheet 10 The goal in this worksheet is to compute a high power of a matrix. For example, bracketleftbigg . 95 . 1 . 1 . 89 bracketrightbigg 500 The process involves eigenvalues and eigenvectors , which I will define by example as they come up, and them more formally in the next worksheet. Part I. The first stage is to solve the system of two equations bracketleftbigg . 95 - λ . 1 . 1 . 89 - λ bracketrightbiggbracketleftbigg x y bracketrightbigg = bracketleftbigg 0 0 bracketrightbigg for the three variables x , y and λ . That’s more than 2 variables, so we don’t use normal algebra to solve this. Instead: Any solution with x = 0 and y = 0 is forbidden. Other solutions exist if and only if the determinant of bracketleftbigg . 95 - λ . 1 . 1 . 89 - λ bracketrightbigg is zero. Therefore: 1. Solve the equation ( . 95 - λ )( . 89 - λ ) - ( . 1)( . 1) = 0 Each solution is called an eigenvalue . 2. Pick one of the eigenvalues, say λ 1 = 1 . 0244. Find one non-zero solution to the system of equations bracketleftbigg . 95 - 1 . 0244 . 1 . 1 . 89 - 1 . 0244 bracketrightbiggbracketleftbigg x y
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
Image of page 2
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