Find the geometric and algebraic multiplicity of each eigenvalue and determine whether A is diagonalizable...
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Algebra
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 AP 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 A 0 2 50 50 0 3 0 00 3 0 0 O 2 Algebraic multiplicity Geometric multiplicity 2 3 Algebraic multiplicity Geometric multiplicity 2 2000 02 0 0 00 3 0 Loo 0 3 O 2 Algebraic multiplicity Geometric multiplicity 2 3 Algebraic multiplicity Geometric multiplicity 2 2 0 0 0 0 200 0 030 003 0 P P 0100 10 10 10 00 0 1 00 1 0 01 0 0 10 50 50 00 0 1 00 1 P P AP OX 2 Algebraic multiplicity Geometric multiplicity 1 3 Algebraic multiplicity 2 Geometric multiplicity 1 A is not diagonalizable P AP OX 2 Algebraic multiplicity Geometric multiplicity 2 X 3 Algebraic multiplicity Geometric multiplicity 2 01 0 0 10 10 10 00 0 1 00 1 0 PAP 2 0 0 0 0 200 0 030 0 0 0 3 O 2 Algebraic multiplicity 2 Geometric multiplicity 1 A 3 Algebraic multiplicity Geometric multiplicity 2 A is not diagonalizable
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