This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 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 = 1 1 , 1 − 1 , 1 2 ....
View
Full
Document
This note was uploaded on 12/08/2010 for the course SPMS MAS213 taught by Professor Andrewkricker during the Fall '10 term at Nanyang Technological University.
 Fall '10
 ANDREWKRICKER

Click to edit the document details