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Exercise 3.3.1 In each case find the characteristic poly- nomial, eigenvalues, eigenvectors, and (if possible) an in- vertible matrix P such that P-¹AP is diagonal. 12 a. A = b. A = 32 [ 2-4 - -1 -1 70-4 c. A = 05 0 50-2 1-2 3 e. A = 2 6-6 1 2 -1 ] f. A = 11-3 d. A = 206 1-15 0 1 0 301 200 3 1 1 2 1 1 g. A = -4-2-5 h. A = 0 1 0 225 1 -1 2

Exercise 3.3.1 In each case find the characteristic poly- nomial, eigenvalues, eigenvectors, and (if possible) an in- vertible matrix P such that P-¹AP is diagonal. 12 a. A = b. A = 32 [ 2-4 - -1 -1 70-4 c. A = 05 0 50-2 1-2 3 e. A = 2 6-6 1 2 -1 ] f. A = 11-3 d. A = 206 1-15 0 1 0 301 200 3 1 1 2 1 1 g. A = -4-2-5 h. A = 0 1 0 225 1 -1 2

Calculus For The Life Sciences
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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Exercise 3.3.1 In each case find the characteristic poly- nomial, eigenvalues, eigenvectors, and (if possible) an in- vertible matrix P such that P-¹AP is diagonal. 12 a. A = b. A = 32 [ 2-4 - -1 -1 70-4 c. A = 05 0 50-2 1-2 3 e. A = 2 6-6 1 2 -1 ] f. A = 11-3 d. A = 206 1-15 0 1 0 301 200 3 1 1 2 1 1 g. A = -4-2-5 h. A = 0 1 0 225 1 -1 2
Transcribed Image Text:Exercise 3.3.1 In each case find the characteristic poly- nomial, eigenvalues, eigenvectors, and (if possible) an in- vertible matrix P such that P-¹AP is diagonal. 12 a. A = b. A = 32 [ 2-4 - -1 -1 70-4 c. A = 05 0 50-2 1-2 3 e. A = 2 6-6 1 2 -1 ] f. A = 11-3 d. A = 206 1-15 0 1 0 301 200 3 1 1 2 1 1 g. A = -4-2-5 h. A = 0 1 0 225 1 -1 2
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