3 -2 -2 1 Let A = -2 3 -2 and v = 1 Verify that 5 is an eigenvalue of A and v is an eigenvector. Then orthogonally -2 - 2 3 1 diagonalize A. 1 The number 5 is an eigenvalue of A with eigenvector 1 (Type an exact answer, using radicals as needed.) 1 The vector v = 1 is an eigenvector of A with eigenvalue - 1. 1 (Type an exact answer, using radicals as needed.) Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. Enter the matrices P and D below. (Use a comma to separate matrices as needed. Type exact answers, using radicals as needed. Do not label the matrices.)
3 -2 -2 1 Let A = -2 3 -2 and v = 1 Verify that 5 is an eigenvalue of A and v is an eigenvector. Then orthogonally -2 - 2 3 1 diagonalize A. 1 The number 5 is an eigenvalue of A with eigenvector 1 (Type an exact answer, using radicals as needed.) 1 The vector v = 1 is an eigenvector of A with eigenvalue - 1. 1 (Type an exact answer, using radicals as needed.) Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. Enter the matrices P and D below. (Use a comma to separate matrices as needed. Type exact answers, using radicals as needed. Do not label the matrices.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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
Transcribed Image Text:3 -2 -2
1
Let A = -2
3 -2 and v = 1
Verify that 5 is an eigenvalue of A and v is an eigenvector. Then orthogonally
-2 - 2
3
1
diagonalize A.
1
The number 5 is an eigenvalue of A with eigenvector
1
(Type an exact answer, using radicals as needed.)
1
The vector v = 1 is an eigenvector of A with eigenvalue - 1.
1
(Type an exact answer, using radicals as needed.)
Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. Enter the matrices P and D
below.
(Use a comma to separate matrices as needed. Type exact answers, using radicals as needed. Do not label the matrices.)
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