6. 4 01 Consider A (-2 10). -201 a) Find all the eigenvalues of A b) Find the basis for the eigenspace corresponding to λ = 2 (4m) (6m) 0 0 -2 7. Consider a matrix A (1 2 1) with eigenvalues 1-2, 2, 1. The 10 3 corresponding eigenvectors are: = -1 0 V=2 {(0)+(1) t; r, tЄ R; r = 0, t = 0} 1 0 -2 V= {(1) rr€ R; r = 0} 1 Using the given information, answer the following. a) b) c) Is A diagonalizable? Give a reason for your answer Does A exist? Give a reason for your answer Determine matrix P such that P-1 AP = D. (2m) (2m) (1m) (Dec 2018, MAT263) -2 8. Consider matrix A=(0 31 3 -9 3,where -2 is the smallest eigenvalue. 0 4 2 a) Show that 5 is the other eigenvalue of A (5m) b) Find the eigenvector corresponding to the smallest eigenvalue of A (5m) c) State the algebraic multiplicity and geometric multiplicity when λ = -2

6. 4 01 Consider A (-2 10). -201 a) Find all the eigenvalues of A b) Find the basis for the eigenspace corresponding to λ = 2 (4m) (6m) 0 0 -2 7. Consider a matrix A (1 2 1) with eigenvalues 1-2, 2, 1. The 10 3 corresponding eigenvectors are: = -1 0 V=2 {(0)+(1) t; r, tЄ R; r = 0, t = 0} 1 0 -2 V= {(1) rr€ R; r = 0} 1 Using the given information, answer the following. a) b) c) Is A diagonalizable? Give a reason for your answer Does A exist? Give a reason for your answer Determine matrix P such that P-1 AP = D. (2m) (2m) (1m) (Dec 2018, MAT263) -2 8. Consider matrix A=(0 31 3 -9 3,where -2 is the smallest eigenvalue. 0 4 2 a) Show that 5 is the other eigenvalue of A (5m) b) Find the eigenvector corresponding to the smallest eigenvalue of A (5m) c) State the algebraic multiplicity and geometric multiplicity when λ = -2

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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