Mathematics, 21.05.2021 17:10 shyann78

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. A = [0 0 0 0 0 0 20 0 1]
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]
2. lambda = 0. Algebraic multiplicity = 1, Geometric multiplicity = 2.
lambda = 1. Algebraic multiplicity = Geometric multiplicity = 1. A is not diagonalizable.
3. lambda = 0. Algebraic multiplicity = 2, Geometric multiplicity = 1.
lambda = 1. Algebraic multiplicity = Geometric multiplicity = 1. A is not diagonalizable.
4. 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]
5. 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]

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