1. Consider the operator T : R 2 → R2 such that T(x, y) = (x + y, x + y). (a) Find the eigenvalues ​​of T. (b) Find the eigenspaces of T. (c) Find a spectral decomposition for the canonical matrix of the T operator

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 76E: Define T:P2P2 by T(a0+a1x+a2x2)=(2a0+a1a2)+(a1+2a2)xa2x2. Find the eigenvalues and the eigenvectors...
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1. Consider the operator T : R 2 → R2 such that T(x, y) = (x + y, x + y).
(a) Find the eigenvalues ​​of T. (b) Find the eigenspaces of T. (c) Find a spectral decomposition for the canonical matrix of the T operator.

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