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2 -8 -8 Let A = - 8 2 -8 and v= Verify that 10 is an eigenvalue of A and v is an eigenvector. Then orthogonally diagonalize A - 8 - 8 2 The number 10 is an eigenvalue of A with eigenvector (Type an exact answer, using radicals as needed.) 1 The vector v = 1 is an eigenvector of A with eigenvalueO (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.)

2 -8 -8 Let A = - 8 2 -8 and v= Verify that 10 is an eigenvalue of A and v is an eigenvector. Then orthogonally diagonalize A - 8 - 8 2 The number 10 is an eigenvalue of A with eigenvector (Type an exact answer, using radicals as needed.) 1 The vector v = 1 is an eigenvector of A with eigenvalueO (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
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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2 -8 -8 Let A = - 8 2 -8 and v= Verify that 10 is an eigenvalue of A and v is an eigenvector. Then orthogonally diagonalize A. - 8 -8 2 The number 10 is an eigenvalue of A with eigenvector (Type an exact answer, using radicals as needed.) 1 The vector v = 1 is an eigenvector of A with eigenvalueO (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.)
Transcribed Image Text:2 -8 -8 Let A = - 8 2 -8 and v= Verify that 10 is an eigenvalue of A and v is an eigenvector. Then orthogonally diagonalize A. - 8 -8 2 The number 10 is an eigenvalue of A with eigenvector (Type an exact answer, using radicals as needed.) 1 The vector v = 1 is an eigenvector of A with eigenvalueO (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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