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-
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 30E
Question

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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