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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 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).) 0 0 0 -2 10 - 10 -2 A = 3 0 0 3 O A = -2. Algebraic multiplicity = Geometric multiplicity = 2. A = 3. Algebraic multiplicity = Geometric multiplicity = 2. 0 0 1 0 -2 2 0 0 01 0 -2 0 0 1 -2 P = P'AP = 0 0 0 1 030 0 0 1 0 0 0 3 O A= -2. Algebraic multiplicity = Geometric multiplicity = 2. A= 3. Algebraic multiplicity = Geometric multiplicity = 2. 1 01 -2 0 0 0 10 - 10 10 P = 0 0 0 -2 0 0 P-'AP = 1 0 3 0 0 0 1 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. Ais not diagonalizable.

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 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).) 0 0 0 -2 10 - 10 -2 A = 3 0 0 3 O A = -2. Algebraic multiplicity = Geometric multiplicity = 2. A = 3. Algebraic multiplicity = Geometric multiplicity = 2. 0 0 1 0 -2 2 0 0 01 0 -2 0 0 1 -2 P = P'AP = 0 0 0 1 030 0 0 1 0 0 0 3 O A= -2. Algebraic multiplicity = Geometric multiplicity = 2. A= 3. Algebraic multiplicity = Geometric multiplicity = 2. 1 01 -2 0 0 0 10 - 10 10 P = 0 0 0 -2 0 0 P-'AP = 1 0 3 0 0 0 1 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. Ais not diagonalizable.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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).) 0 0 0 -2 10 - 10 -2 A = 3 0 0 3 O A = -2. Algebraic multiplicity = Geometric multiplicity = 2. A= 3. Algebraic multiplicity = Geometric multiplicity = 2. -2 0 0 01 1 0 -2 2 0 1 1 0 0 -2 0 0 P = p'AP = 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. 0 0 0 01 1 0 - 10 10 -2 0 -2 0 0 P = 0 0 p'AP = 1 0 3 0 0 0 1 0 0 3 O A= -2. Algebraic multiplicity = Geometric multiplicity = 1. A= 3. Algebraic multiplicity = 2, Geometric multiplicity = 1. A is 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 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).) 0 0 0 -2 10 - 10 -2 A = 3 0 0 3 O A = -2. Algebraic multiplicity = Geometric multiplicity = 2. A= 3. Algebraic multiplicity = Geometric multiplicity = 2. -2 0 0 01 1 0 -2 2 0 1 1 0 0 -2 0 0 P = p'AP = 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. 0 0 0 01 1 0 - 10 10 -2 0 -2 0 0 P = 0 0 p'AP = 1 0 3 0 0 0 1 0 0 3 O A= -2. Algebraic multiplicity = Geometric multiplicity = 1. A= 3. Algebraic multiplicity = 2, Geometric multiplicity = 1. A is not diagonalizable. O A = -2. Algebraic multiplicity = 2, Geometric multiplicity = 1. A= 3. Algebraic multiplicity = Geometric multiplicity = 2. Ais not diagonalizable.
O A= -2. Algebraic multiplicity = Geometric multiplicity = 2. A= 3. Algebraic multiplicity = Geometric multiplicity = 2. 0 0 1 0 -2 2 1 2 0 0 2 P = 0 0 P'AP : 1 0 0 -3 0 0 1 0 0 0 0 -3
Transcribed Image Text:O A= -2. Algebraic multiplicity = Geometric multiplicity = 2. A= 3. Algebraic multiplicity = Geometric multiplicity = 2. 0 0 1 0 -2 2 1 2 0 0 2 P = 0 0 P'AP : 1 0 0 -3 0 0 1 0 0 0 0 -3
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