(19 1. Let T V V be a linear operator on the vector space V over Q that has characteristic polynomial XT(x) = -(x-1)4(x-2)3(x+1)2 and has minimal polynomial (r - 1)2(x-2)²(x + 1)². Find the possible Jordan normal forms of T. (Arrange the Jordan blocks so that the eigenvalues appear on the diagonal in a non-increasing sequence.)
(19 1. Let T V V be a linear operator on the vector space V over Q that has characteristic polynomial XT(x) = -(x-1)4(x-2)3(x+1)2 and has minimal polynomial (r - 1)2(x-2)²(x + 1)². Find the possible Jordan normal forms of T. (Arrange the Jordan blocks so that the eigenvalues appear on the diagonal in a non-increasing sequence.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 43E
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
Transcribed Image Text:(19 1. Let T V V be a linear operator on the vector space V over Q that has characteristic
polynomial XT(x) = -(x-1)4(x-2)3(x+1)2 and has minimal polynomial (r - 1)2(x-2)²(x + 1)². Find
the possible Jordan normal forms of T. (Arrange the Jordan blocks so that the eigenvalues appear on the
diagonal in a non-increasing sequence.)
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