problemset8 - MAS 213 Linear Algebra II Problem list for...

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

View Full Document Right Arrow Icon
MAS 213: Linear Algebra II. Problem list for Week #8. Tutorial on the 2nd of November. This week’s topics: The definition of a diagonalizable operator. The definition of a diagonalizable matrix. The definition of eigenvalues and eigenvectors. The characteristic polynomial of a matrix. Determining the eigenvalues and eigenvectors of a matrix. Tutorial problems: Problem 1: (Problem 5.1.2, various parts, from [FIS].) In this problem you are given a linear operator T ∈ L ( V ) on some vector space V , and a basis β for the vector space. The problem is to calculate the matrix representation of the operator with respect to the given basis, and so determine whether the basis is a basis of eigenvectors for the operator. (i) V = P 1 ( R ), T ( a + bx ) = (6 a 6 b ) + (12 a 11 b ) x , and β = { 3 + 4 x, 2 + 3 x } . (ii) V = R 3 , T a b c = 3 a + 2 b 2 c 4 a 3 b + 2 c c , and β = 0 1 1 , 1 1 0 , 1 0 2 .
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