3. Suppose L : R² → R² is a linear transformation. (a) If L(ej) = e + €2 and L(e,) = e¡ + e2, verify that e, + e, is an eigenvector of L. Find the corresponding eigenvalue. (b) Find the characteristic polynomial of L and then find another eigenvalue of L. (c) Find an eigenvector for the second eigenvalue you found in part (b).
3. Suppose L : R² → R² is a linear transformation. (a) If L(ej) = e + €2 and L(e,) = e¡ + e2, verify that e, + e, is an eigenvector of L. Find the corresponding eigenvalue. (b) Find the characteristic polynomial of L and then find another eigenvalue of L. (c) Find an eigenvector for the second eigenvalue you found in part (b).
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 28EQ
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