Given the below matrix, determine the following. Show all work. a. The eigenvalues for the matrix. b. The eigenvectors for the matrix. c. If there are repeated eigenvalues, determine the algebraic multiplicity, geometric multiplicity, and the defect for the repeated eigenvalue. [4 -1 A = 2 L2 1 6 -1 8]

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
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Given the below matrix, determine the following. Show all work.
a. The eigenvalues for the matrix.
b. The eigenvectors for the matrix.
c. If there are repeated eigenvalues, determine the algebraic multiplicity, geometric
multiplicity, and the defect for the repeated eigenvalue.
[4
A = 2
L2
-1 6
1 6
-1
8]
Transcribed Image Text:Given the below matrix, determine the following. Show all work. a. The eigenvalues for the matrix. b. The eigenvectors for the matrix. c. If there are repeated eigenvalues, determine the algebraic multiplicity, geometric multiplicity, and the defect for the repeated eigenvalue. [4 A = 2 L2 -1 6 1 6 -1 8]
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