Find the geometric and algebraic multiplicity of each eigenvalue, and determine

Question

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). ) A = [0 0 0 0 0 0 20 0 1] lambda = 0. Algebraic multiplicity = Geometric multiplicity = 2. lambda = 1. Algebraic multiplicity = Geometric multiplicity = 1. p = [-1 0 0 0 1 0 20 0 1], P-1AP = [0 0 0 0 0 0 0 0 1] lambda = 0. Algebraic multiplicity = 1, Geometric multiplicity = 2. lambda = 1. Algebraic multiplicity = Geometric multiplicity = 1. A is not diagonalizable. lambda = 0. Algebraic multiplicity = 2, Geometric multiplicity = 1. lambda = 1. Algebraic multiplicity = Geometric multiplicity = 1. A is not diagonalizable. lambda = 0. Algebraic multiplicity = Geometric multiplicity = 2. lambda = 1. Algebraic multiplicity = Geometric multiplicity = 1. P= [-1 0 0 0 0 1 20 0 1], P-1AP = [1 0 0 0 0 0 0 0 1] lambda = 0. Algebraic multiplicity = Geometric multiplicity = 2. lambda = 1. Algebraic multiplicity = Geometric multiplicity = 1. P =[-20 0 0 0 1 0 1 0 1],P-1AP = [0 0 0 0 0 0 0 0 1]

Explanation / Answer

Option c

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