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-2 The matrix A = 0-87 8 4 2 2 0 6 has a single real eigenvalue X = 2 with algebraic multiplicity three. (a) Find a basis for the associated eigenspace. 00 Basis = { (b) Is the matrix A defective? OA. A is defective because the geometric multiplicity of the eigenvalue is less than the algebraic multiplicity OB. A is not defective because the eigenvectors are linearly independent c. A is defective because it has only one eigenvalue OD. A is not defective because the eigenvalue has algebraic multiplicity three

-2 The matrix A = 0-87 8 4 2 2 0 6 has a single real eigenvalue X = 2 with algebraic multiplicity three. (a) Find a basis for the associated eigenspace. 00 Basis = { (b) Is the matrix A defective? OA. A is defective because the geometric multiplicity of the eigenvalue is less than the algebraic multiplicity OB. A is not defective because the eigenvectors are linearly independent c. A is defective because it has only one eigenvalue OD. A is not defective because the eigenvalue has algebraic multiplicity three

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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-2 0-87 2 8 0 6 has a single real eigenvalue X = 2 with algebraic multiplicity three. (a) Find a basis for the associated eigenspace. The matrix 4 = 4 2 Basis = {} (b) Is the matrix A defective? OA. A is defective because the geometric multiplicity of the eigenvalue is less than the algebraic multiplicity OB. A is not defective because the eigenvectors are linearly independent Oc. A is defective because it has only one eigenvalue OD. A is not defective because the eigenvalue has algebraic multiplicity three
Transcribed Image Text:-2 0-87 2 8 0 6 has a single real eigenvalue X = 2 with algebraic multiplicity three. (a) Find a basis for the associated eigenspace. The matrix 4 = 4 2 Basis = {} (b) Is the matrix A defective? OA. A is defective because the geometric multiplicity of the eigenvalue is less than the algebraic multiplicity OB. A is not defective because the eigenvectors are linearly independent Oc. A is defective because it has only one eigenvalue OD. A is not defective because the eigenvalue has algebraic multiplicity three
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