L: R² → R² is a linear map. If the underlying 2 × 2 matrix A has trace 4 and determinant 4, does L have any non-trivial fixed points?¹ Justify your answer. (Hint: a linear map L has non-trivial fixed points if and only if λ = 1 is an eigenvalue of L).

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 55EQ
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14. L : R² → R² is a linear map. If the underlying 2 × 2 matrix A has trace 4 and
determinant 4, does L have any non-trivial fixed points? Justify your answer.
(Hint: a linear map L has non-trivial fixed points if and only if λ = 1 is an
eigenvalue of L).
Transcribed Image Text:14. L : R² → R² is a linear map. If the underlying 2 × 2 matrix A has trace 4 and determinant 4, does L have any non-trivial fixed points? Justify your answer. (Hint: a linear map L has non-trivial fixed points if and only if λ = 1 is an eigenvalue of L).
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