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Find the law of linear transformation T : R 3 → R 3 such that 1 and −1 are the eigenvalues ​​of T, S1 = {(a, b, a) : a, b ∈ R} is the eigenspace associated with the eigenvalue 1, and S−1 = {(a, −a, −a) : a ∈ R} is the eigenspace associated with the eigenvalue −1.

Find the law of linear transformation T : R 3 → R 3 such that 1 and −1 are the eigenvalues ​​of T, S1 = {(a, b, a) : a, b ∈ R} is the eigenspace associated with the eigenvalue 1, and S−1 = {(a, −a, −a) : a ∈ R} is the eigenspace associated with the eigenvalue −1.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 36EQ: Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two...
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Find the law of linear transformation T : R 3 → R 3 such that
1 and −1 are the eigenvalues ​​of T,
S1 = {(a, b, a) : a, b ∈ R} is the eigenspace associated with the eigenvalue 1, and
S−1 = {(a, −a, −a) : a ∈ R} is the eigenspace associated with the eigenvalue −1.

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