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

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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 .

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• Fall '10
• ANDREWKRICKER

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