15. Let T: P, P, be defined by T(a, + a,x+ a,x²) = (5a, + 6a1 + 2a,) - (a, + 8a,)x + (a, – 2a,)x² a. Find the eigenvalues of T. b. Find bases for the eigenspaces of T.
15. Let T: P, P, be defined by T(a, + a,x+ a,x²) = (5a, + 6a1 + 2a,) - (a, + 8a,)x + (a, – 2a,)x² a. Find the eigenvalues of T. b. Find bases for the eigenspaces of T.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:15. Let T : P, → P, be defined by
T(a, + a,x + a,x²) = (5a, + 6a, + 2a,)
%3D
- (a, + 8a,)x + (a, – 2a,)x²
a. Find the eigenvalues of T.
b. Find bases for the eigenspaces of T.
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