Question

Algebraic multiplicity of the eigenvalue is given and then find geometric multiplicity

Answer 1

Answer:

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Step-by-step explanation:

What is the algebraic multiplicity of an eigenvalue?

Definition: the algebraic multiplicity of an eigenvalue e is the power to which (λ – e) divides the characteristic polynomial. Definition: the geometric multiplicity of an eigenvalue is the number of linearly independent eigenvectors associated with it. That is, it is the dimension of the nullspace of A – eI.

What is geometric and algebraic multiplicity?

The dimension of the eigenspace of λ is called the geometric multiplicity of λ. Remember that the multiplicity with which an eigenvalue appears is called the algebraic multi- plicity of λ: The algebraic multiplicity is larger or equal than the geometric multiplicity.