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).) -200 0 0-2 50-50 A = 0 0 3 0 0 00 3 0 1 0 10-10 10 01 01--2. Algebraic multiplicity - Geometric multiplicity = 2 X=3. Algebraic multiplicity Geometric multiplicity = 2. [200 02 0 0 P= P-AP = 00 00 0 1 1 0 00-3 0 Lo o 0-3 OA=-2. Algebraic multiplicity - Geometric multiplicity = 2. A 3. Algebraic multiplicity Geometric multiplicity = 2 0 1 0 0 10-50 50 -2 000 0-200 P= PAP = 00 0 1 00 1 0 0030 0 0 0 3 OA=-2. Algebraic multiplicity - Geometric multiplicity = 1. = 3. Algebraic multiplicity = 2, Geometric multiplicity = 1. A is not diagonalizable. OX=-2. Algebraic multiplicity - Geometric multiplicity = 2. A=3. Algebraic multiplicity = Geometric multiplicity = 2 0 1 0 0] 000] -2 10-10 P = 00 10 01 0-200 P-'AP = 0030 00 1 0003 O=-2. Algebraic multiplicity-2, Geometric multiplicity = 1 1=3. Algebraic multiplicity - Geometric multiplicity = 2. A is not diagonalizable.