DEFINITION: algebraic multiplicity of the eigenvalue A is the multiplicity of A as a root of the characteristic equation p(X) = 0. DEFINITION: geometric multiplicity of the eigenvalue A is the number of linearly independent eigenvectors associated with A. Ex Consider the matrix 3 1 1 1 31 1 1 3 R= It is known that p(A) = -(A – 5)(A – 2)². Determine the algebraic multiplicity and the geometric multiplicity of each eigenvalue.

DEFINITION: algebraic multiplicity of the eigenvalue A is the multiplicity of A as a root of the characteristic equation p(X) = 0. DEFINITION: geometric multiplicity of the eigenvalue A is the number of linearly independent eigenvectors associated with A. Ex Consider the matrix 3 1 1 1 31 1 1 3 R= It is known that p(A) = -(A – 5)(A – 2)². Determine the algebraic multiplicity and the geometric multiplicity of each eigenvalue.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.1: Eigenvalues And Eigenvectors

Problem 64E

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