-λ = -2. Algebraic multiplicity = 2, Geometric multiplicity = 1.λ = 3. Algebraic multiplicity = Geometric multiplicity = 2.A is not diagonalizable. -λ = -2. Algebraic multiplicity = Geometric multiplicity = 1.λ = 3. Algebraic multiplicity = 2, Geometric multiplicity = 1.A is not diagonalizable. O A = -2. Algebraic multiplicity = Geometric multiplicity = 2.1 = 3. Algebraic multiplicity = Geometric multiplicity = 2.0 10 0-20 0 01 0 -1 10 -2 0 0p-'AP =P =0 00 3 00 10 010]0 0 3O A = -2. Algebraic multiplicity = Geometric multiplicity = 2.A = 3. Algebraic multiplicity = Geometric multiplicity = 2.0 10 02 01 0 -1 10 2P =p-'AP =%3D0 00 10 0-30 01 00 00 -3|O A = -2. Algebraic multiplicity = 2, Geometric multiplicity = 1.A = 3. Algebraic multiplicity = Geometric multiplicity = 2.A is not diagonalizable. Find the geometric and algebraic multiplicity of each eigenvalue, and determine whether A is diagonalizable. If so, find a matrix P thatdiagonalizes A, and determine P1AP(Notice that the order of the eigenvalues and corresponding eigenvectors can be different from yours and that the eigenvectors aredefined accurately to the factor (sign).)-20 00 -2 5 -5A =0 30 03O A = -2. Algebraic multiplicity = Geometric multiplicity = 2.A = 3. Algebraic multiplicity = Geometric multiplicity = 2.0.10 0-20 0 01P =-2 0 00 - 55p-'AP =0 00 10301 00 0 3

The eigenvalue for the given matrix is: -2, -2 , 3, 3

Find the geometric and algebraic multiplicity of each eigenvalue, and determine whether A is diagonalizable. If so, find a matrix P that diagonalizes A, and determine P-1AP (Notice that the order of the eigenvalues and corresponding eigenvectors can be different from yours and that the eigenvectors are defined accurately to the factor (sign).) -2 0 0 0 -2 5 -5 A = 0 3 0 0 3 O A = -2. Algebraic multiplicity = Geometric multiplicity = 2. A = 3. Algebraic multiplicity = Geometric multiplicity = 2. 0 0 -2 0 0 0 10 -5 5 0 -2 0 0 0 3 0 P = P-'AP = 0 0 0 1

Find the geometric and algebraic multiplicity of each eigenvalue, and determine whether A is diagonalizable. If so, find a matrix P that diagonalizes A, and determine P-1AP (Notice that the order of the eigenvalues and corresponding eigenvectors can be different from yours and that the eigenvectors are defined accurately to the factor (sign).) -2 0 0 0 -2 5 -5 A = 0 3 0 0 3 O A = -2. Algebraic multiplicity = Geometric multiplicity = 2. A = 3. Algebraic multiplicity = Geometric multiplicity = 2. 0 0 -2 0 0 0 10 -5 5 0 -2 0 0 0 3 0 P = P-'AP = 0 0 0 1

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.5: Iterative Methods For Computing Eigenvalues

Problem 5EQ

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