In Exercises 5 and 6, the matrix A is factored in the form PDP-¹. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 5. 2 2 1 1 3 1 = 1 1 1 1 2 2 1 2 0 -1 0 -1 500 1/4 1/2 1/4] 0 1 0 1/4 1/2-3/4 001 1/4-1/2 1/4

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 14E: In exercise 14 and 15, each 22matrix has only one eigenvalue. Find the eigenvalue and the...
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In Exercises 5 and 6, the matrix A is factored in the form PDP-¹. Use the
Diagonalization Theorem to find the eigenvalues of A and a basis for each
eigenspace.
5.
22
1 3 1 =
1
2 2
1
1
1 -1
1 2
0 -1
0
500
0 1 0
001
[1/4 1/2 1/4]
1/4 1/2-3/4
1/4-1/2 1/4
Transcribed Image Text:In Exercises 5 and 6, the matrix A is factored in the form PDP-¹. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 5. 22 1 3 1 = 1 2 2 1 1 1 -1 1 2 0 -1 0 500 0 1 0 001 [1/4 1/2 1/4] 1/4 1/2-3/4 1/4-1/2 1/4
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