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2. Let T = 1 0 2-3 0 3 and denote I3 = 0 1 0 001 (c) Express an arbitrary vector v = nation of eigenvectors of T. . (a) i). Calculate det (T-213) for any a to find the characteristic polynomial of T; ii). Determine the eigenvalues of T. (b) Find an eigenvector of T associated with each of the eigenvalues of T. a b in R³, where a, b, c ER, as a linear combi-

2. Let T = 1 0 2-3 0 3 and denote I3 = 0 1 0 001 (c) Express an arbitrary vector v = nation of eigenvectors of T. . (a) i). Calculate det (T-213) for any a to find the characteristic polynomial of T; ii). Determine the eigenvalues of T. (b) Find an eigenvector of T associated with each of the eigenvalues of T. a b in R³, where a, b, c ER, as a linear combi-

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 38EQ
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2. Let T = -2 1 1 2-3 1 0 0 3 and denote 13 = 1 0 0 1 0 0 001 (a) i). Calculate det (T-xI3) for any r to find the characteristic polynomial of T; ii). Determine the eigenvalues of T. (b) Find an eigenvector of T associated with each of the eigenvalues of T. a (c) Express an arbitrary vector v = b in R³, where a, b, c ER, as a linear combi- C nation of eigenvectors of T.
Transcribed Image Text:2. Let T = -2 1 1 2-3 1 0 0 3 and denote 13 = 1 0 0 1 0 0 001 (a) i). Calculate det (T-xI3) for any r to find the characteristic polynomial of T; ii). Determine the eigenvalues of T. (b) Find an eigenvector of T associated with each of the eigenvalues of T. a (c) Express an arbitrary vector v = b in R³, where a, b, c ER, as a linear combi- C nation of eigenvectors of T.
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