[-1 0 87 -4 3 8 -2 07 has a single real elgenvalue λ = 3 with algebraic multiplicity three. (a) Find a basis for the associated eigenspace. The matrix A= Basis = (b) is the matrix A defective? DA. A is defective because the geometric multiplicity of the eigenvalue is less than the algebraic multiplicity OB. A is not defective because the elgenvectors 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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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T-1 0 81
The matrix A = -4 3 8
-2 07
has a single real elgenvalue λ = 3 with algebraic multiplicity three.
(a) Find a basis for the associated elgenspace.
Basis =
(b) Is the matrix A defective?
DA. A is defective because the geometric multiplicity of the eigenvalue is less than the algebraic multiplicity
OB. A is not defective because the elgenvectors 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:T-1 0 81 The matrix A = -4 3 8 -2 07 has a single real elgenvalue λ = 3 with algebraic multiplicity three. (a) Find a basis for the associated elgenspace. Basis = (b) Is the matrix A defective? DA. A is defective because the geometric multiplicity of the eigenvalue is less than the algebraic multiplicity OB. A is not defective because the elgenvectors 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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