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15. Let T: P2 → P2 be defined by T(a, + a,x + a,x²) = (5a, + 6a, + 2a2) %3D - (a, + 8a,)x + (a, – 2a,)x² | a. Find the eigenvalues of T. b. Find bases for the eigenspaces of T.

15. Let T: P2 → P2 be defined by T(a, + a,x + a,x²) = (5a, + 6a, + 2a2) %3D - (a, + 8a,)x + (a, – 2a,)x² | a. Find the eigenvalues of T. b. Find bases for the eigenspaces of T.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
Problem 31EQ
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15. Let T: P2 → P2 be defined by T(a, + a,x + azx²) = (5a, + 6a, + 2a,) - (a, + 8a,)x + (a, – 2a,)x² | a. Find the eigenvalues of T. b. Find bases for the eigenspaces of T.
Transcribed Image Text:15. Let T: P2 → P2 be defined by T(a, + a,x + azx²) = (5a, + 6a, + 2a,) - (a, + 8a,)x + (a, – 2a,)x² | a. Find the eigenvalues of T. b. Find bases for the eigenspaces of T.
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