EIGENVALUES AND EIGENVECTORS 1 00 1. Consider the matrix A = ( -1 0 1). 4 -8 6 2. 3. a) Show that the eigenvalues of A are 1, 2 and 4 b) (4m) Find the basis for the eigenspace corresponding to λ = 1. State its geometric multiplicity. (6m) 3 20 Consider matrix A = (2 3 0). 005 a) Find the eigenvalues of A b) c) (Dec 2019, MAT263) (5m) The basis for the eigenspace of A corresponding to the largest eigenvalue is 1 0 E=5 = {(1).( 0)} Determine the basis for the eigenspace of A 0 1 . corresponding to the smallest eigenvalue Is A diagonalizable? Give a reason for your answer. (6m) (2m) (Dec 2019, MAT423) 506 Consider the matrix A = ( 2 1 2). 130 a) Find the eigenvalues of matrix A (5m) b) Find the basis for the eigenspace corresponding to the smallest eigenvalue of A (5m)

EIGENVALUES AND EIGENVECTORS 1 00 1. Consider the matrix A = ( -1 0 1). 4 -8 6 2. 3. a) Show that the eigenvalues of A are 1, 2 and 4 b) (4m) Find the basis for the eigenspace corresponding to λ = 1. State its geometric multiplicity. (6m) 3 20 Consider matrix A = (2 3 0). 005 a) Find the eigenvalues of A b) c) (Dec 2019, MAT263) (5m) The basis for the eigenspace of A corresponding to the largest eigenvalue is 1 0 E=5 = {(1).( 0)} Determine the basis for the eigenspace of A 0 1 . corresponding to the smallest eigenvalue Is A diagonalizable? Give a reason for your answer. (6m) (2m) (Dec 2019, MAT423) 506 Consider the matrix A = ( 2 1 2). 130 a) Find the eigenvalues of matrix A (5m) b) Find the basis for the eigenspace corresponding to the smallest eigenvalue of A (5m)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 8E

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