c) Find an ordered basis y for V consisting only of eigenvectors and find (Ty. d) Find an invertible matrix P and a diagonal matrix D such that PT|,P = D. %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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I need C and D part solution just

2.
Let 3 = {e1, e2, es} be the standard basis for V = R°. Let T be the linear
operator on V defined by
T(a, b, c) = (4c, 26, a).
%3D
a) Find [T]; and the characteristic polynomial of T.
b) Find an ordered basis for each eigenspace of T.
Transcribed Image Text:2. Let 3 = {e1, e2, es} be the standard basis for V = R°. Let T be the linear operator on V defined by T(a, b, c) = (4c, 26, a). %3D a) Find [T]; and the characteristic polynomial of T. b) Find an ordered basis for each eigenspace of T.
c) Find an ordered basis y for V consisting only of eigenvectors and find (T]y.
d) Find an invertible matrix P and a diagonal matrix D such that P-1TP = D.
Transcribed Image Text:c) Find an ordered basis y for V consisting only of eigenvectors and find (T]y. d) Find an invertible matrix P and a diagonal matrix D such that P-1TP = D.
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