Let A be an n xn matrix, let I be the n x n identity matrix, and suppose that x E R" is an eigenvector of A corresponding to the eigenvalue A = 4. Let B = 2A? - 18A + 401. (a) Verify (to yourself) that x is an eigenvector of B and find the corresponding eigenvalue u. What is u? u = (b) What is det (B)? det(B)

Let A be an n xn matrix, let I be the n x n identity matrix, and suppose that x E R" is an eigenvector of A corresponding to the eigenvalue A = 4. Let B = 2A? - 18A + 401. (a) Verify (to yourself) that x is an eigenvector of B and find the corresponding eigenvalue u. What is u? u = (b) What is det (B)? det(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 24EQ

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