As you can check, the matrix A = 1 -1 -2 -2 has an eigenvalue -1 with eigenvector-2 23/1 -4 4 7 and an eigenvalue 3 of multiplicity 2 with eigenvector A scalar multiples of 1 solving (A-31)₂ = ₁. Write v2 below: - A 1 1 -1 but all other eigenvectors for X = 3 are 12 so A has a defect of 1. Find a generalized eigenvector 2 for X = 3 by

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.5: Eigenvalues And Eigenvectors
Problem 15E
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As you can check, the matrix A
=
and an eigenvalue 3 of multiplicity 2 with eigenvector
scalar multiples of 1
1
-1 -2 -2 has an eigenvalue -1 with eigenvector-2
23/1
-4
4
7
A
A
1
solving (A-31)₂ = ₁. Write ₂ below:
-
1
G
-1 but all other eigenvectors for λ = 3 are
so A has a defect of 1. Find a generalized eigenvector 2 for λ = 3 by
Transcribed Image Text:As you can check, the matrix A = and an eigenvalue 3 of multiplicity 2 with eigenvector scalar multiples of 1 1 -1 -2 -2 has an eigenvalue -1 with eigenvector-2 23/1 -4 4 7 A A 1 solving (A-31)₂ = ₁. Write ₂ below: - 1 G -1 but all other eigenvectors for λ = 3 are so A has a defect of 1. Find a generalized eigenvector 2 for λ = 3 by
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