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Part (a) Determine all values of h such that the matrix 5 -3 -1 1 2 3 -1 A = 1-2 2 5 1 3 h has eigenvalue 3. In each solution, the two occurrences of h in A have to be assigned the same value. Find exact solutions, not numerical approximations. Use the simplest possible method. Hint: Use a suitable determinant to obtain a polynomial equation for h.

Part (a) Determine all values of h such that the matrix 5 -3 -1 1 2 3 -1 A = 1-2 2 5 1 3 h has eigenvalue 3. In each solution, the two occurrences of h in A have to be assigned the same value. Find exact solutions, not numerical approximations. Use the simplest possible method. Hint: Use a suitable determinant to obtain a polynomial equation for h.

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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Part (a) Determine all values of h such that the matrix 5 -3 -1 1 2 3 -1 A = 1-2 2 5 1 3 h has eigenvalue 3. In each solution, the two occurrences of h in A have to be assigned the same value. Find exact solutions, not numerical approximations. Use the simplest possible method. Hint: Use a suitable determinant to obtain a polynomial equation for h.
Transcribed Image Text:Part (a) Determine all values of h such that the matrix 5 -3 -1 1 2 3 -1 A = 1-2 2 5 1 3 h has eigenvalue 3. In each solution, the two occurrences of h in A have to be assigned the same value. Find exact solutions, not numerical approximations. Use the simplest possible method. Hint: Use a suitable determinant to obtain a polynomial equation for h.
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