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Theorem (Geometric and Algebraic Multiplicity):
If A is a square matrix, then:
a) For every eigenvalue of A, the geometric multiplicity is less than or equal to the algebraic multiplicity
b) A is diagonalizable if and only if the geometric multiplicity is equal to the algebraic multiplicity for every eigenvalue.
Q. For the matrices below, determine the algebraic and geometric multiplicity of their eigenvalues.
#Eigenvalues #Eigenvectors #LinearAlgebra
