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Find the geometric and algebraic multiplicity of each eigenvalue, and determine whether A is diagonalizable. If so, find a matrix Pthat diagonalizes A, and determine pAP (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 -2 45 -45 A = 3. 3 O A= -2. Algebraic multiplicity = Geometric multiplicity = 2. A= 3. Algebraic multiplicity = Geometric multiplicity = 2. 0 1 0 0 [2 0 P = 10 -9 9 0 2 pAP = 0 1 1 0 0 0 -3 0 0 0 0 0 -3 O A= -2. Algebraic multiplicity = Geometric multiplicity = 2. A = 3. Algebraic multiplicity = Geometric multiplicity = 2. -2 0 0 01 0 -2 00 0 3 0 0 0 3] 0 1 0 0 10 -9 9 P = p'AP = 00 0 0 1 0 O A= -2. Algebraic multiplicity = Geometric multiplicity = 2. A= 3. Algebraic multiplicity = Geometric multiplicity = 2. [0 1 0 0 -2 0 0 0] 10 -45 45 0 0 0 -200 p'AP = 1 P = 030 0 0 1 0 0 0 3 O A= -2. Algebraic multiplicity = Geometric multiplicity = 1. A = 3. Algebraic multiplicity = 2, Geometric multiplicity = 1. Ais not diagonalizable. 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 Pthat diagonalizes A, and determine pAP (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 -2 45 -45 A = 3. 3 O A= -2. Algebraic multiplicity = Geometric multiplicity = 2. A= 3. Algebraic multiplicity = Geometric multiplicity = 2. 0 1 0 0 [2 0 P = 10 -9 9 0 2 pAP = 0 1 1 0 0 0 -3 0 0 0 0 0 -3 O A= -2. Algebraic multiplicity = Geometric multiplicity = 2. A = 3. Algebraic multiplicity = Geometric multiplicity = 2. -2 0 0 01 0 -2 00 0 3 0 0 0 3] 0 1 0 0 10 -9 9 P = p'AP = 00 0 0 1 0 O A= -2. Algebraic multiplicity = Geometric multiplicity = 2. A= 3. Algebraic multiplicity = Geometric multiplicity = 2. [0 1 0 0 -2 0 0 0] 10 -45 45 0 0 0 -200 p'AP = 1 P = 030 0 0 1 0 0 0 3 O A= -2. Algebraic multiplicity = Geometric multiplicity = 1. A = 3. Algebraic multiplicity = 2, Geometric multiplicity = 1. Ais not diagonalizable. O A = -2. Algebraic multiplicity = 2, Geometric multiplicity = 1. A = 3. Algebraic multiplicity = Geometric multiplicity = 2. A is not diagonalizable.

Linear Algebra: A Modern Introduction
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 16EQ
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Find the geometric and algebraic multiplicity of each eigenvalue, and determine whether A is diagonalizable. If so, find a matrix Pthat diagonalizes A, and determine PAP (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 -2 45 -45 A = 3 O A = -2. Algebraic multiplicity = Geometric multiplicity = 2. A= 3. Algebraic multiplicity = Geometric multiplicity = 2. 0 1 10 -9 9 [2 0 0 2 0 0 -3 0 0 P = p'AP = 0 1 1 0 0 0 0 0 0 -3 O A= -2. Algebraic multiplicity = Geometric multiplicity = 2. A = 3. Algebraic multiplicity = Geometric multiplicity = 2. 0 0 0] 0 -2 0 0 0 3 0 0 0 3] 0 1 0 0 -2 10 -9 9 P = p-'AP = 0 0 0 0 1 0 O A= -2. Algebraic multiplicity = Geometric multiplicity = 2. A= 3. Algebraic multiplicity = Geometric multiplicity = 2. 0 1 0 0 -2 0 0 0] 10 -45 45 0 0 0 -2 0 0 p'AP = 1 P = 030 0 0 1 0 0 03 O A= -2. Algebraic multiplicity = Geometric multiplicity = 1. A = 3. Algebraic multiplicity = 2, Geometric multiplicity = 1. Ais not diagonalizable. O A= -2. Algebraic multiplicity = 2, Geometric multiplicity = 1. A = 3. Algebraic multiplicity = Geometric multiplicity = 2. Ais not diagonalizable.
Transcribed Image Text:Find the geometric and algebraic multiplicity of each eigenvalue, and determine whether A is diagonalizable. If so, find a matrix Pthat diagonalizes A, and determine PAP (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 -2 45 -45 A = 3 O A = -2. Algebraic multiplicity = Geometric multiplicity = 2. A= 3. Algebraic multiplicity = Geometric multiplicity = 2. 0 1 10 -9 9 [2 0 0 2 0 0 -3 0 0 P = p'AP = 0 1 1 0 0 0 0 0 0 -3 O A= -2. Algebraic multiplicity = Geometric multiplicity = 2. A = 3. Algebraic multiplicity = Geometric multiplicity = 2. 0 0 0] 0 -2 0 0 0 3 0 0 0 3] 0 1 0 0 -2 10 -9 9 P = p-'AP = 0 0 0 0 1 0 O A= -2. Algebraic multiplicity = Geometric multiplicity = 2. A= 3. Algebraic multiplicity = Geometric multiplicity = 2. 0 1 0 0 -2 0 0 0] 10 -45 45 0 0 0 -2 0 0 p'AP = 1 P = 030 0 0 1 0 0 03 O A= -2. Algebraic multiplicity = Geometric multiplicity = 1. A = 3. Algebraic multiplicity = 2, Geometric multiplicity = 1. Ais not diagonalizable. O A= -2. Algebraic multiplicity = 2, Geometric multiplicity = 1. A = 3. Algebraic multiplicity = Geometric multiplicity = 2. Ais not diagonalizable.
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