Problemset8 - MAS 213 Linear Algebra II Problem list for Week#8 Tutorial on the 2nd of November This week’s topics • The definition of a

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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      ....
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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.

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Problemset8 - MAS 213 Linear Algebra II Problem list for Week#8 Tutorial on the 2nd of November This week’s topics • The definition of a

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