1 1 3 4. Matrix B = (2 60) 657 eigenvectors are as follows: has eigenvalues 2=-1.5, 10. The corresponding 17 V1 (1), v 2=5 λ=10 = ( 3/ 1 1 a) Find the eigenvalues of B* and the corresponding eigenvectors (3m) b) Is B diagonalizable? Give a reason for your answer. (1m) c) Is B an invertible matrix? Give a reason for your answer. (1m) (June 2019, MAT263) 00-2 5. Consider the matrix A = ( 1 2 1). 103 a) Find all eigenvalues of A (5m) b) Find the basis for the eigenspace corresponding to the largest eigenvalue of A obtained in a) (5m) c) State the algebraic multiplicity and geometric multiplicity for the largest eigenvalue of A (2m) (June 2019, MAT423)

1 1 3 4. Matrix B = (2 60) 657 eigenvectors are as follows: has eigenvalues 2=-1.5, 10. The corresponding 17 V1 (1), v 2=5 λ=10 = ( 3/ 1 1 a) Find the eigenvalues of B* and the corresponding eigenvectors (3m) b) Is B diagonalizable? Give a reason for your answer. (1m) c) Is B an invertible matrix? Give a reason for your answer. (1m) (June 2019, MAT263) 00-2 5. Consider the matrix A = ( 1 2 1). 103 a) Find all eigenvalues of A (5m) b) Find the basis for the eigenspace corresponding to the largest eigenvalue of A obtained in a) (5m) c) State the algebraic multiplicity and geometric multiplicity for the largest eigenvalue of A (2m) (June 2019, MAT423)

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 41EQ

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