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Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: A = 2 with eigenvector = and generalized eigenvector = Write the solution to the linear system' = Ar in the following forms. A. In eigenvalue/eigenvector form: [x] = ₁ C1 ]+[ ]). 3. In fundamental matrix form: [x]- C. As two equations: (write "c1" and "c2" for c₁ and c₂) x(t) = y(t) = []

Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: A = 2 with eigenvector = and generalized eigenvector = Write the solution to the linear system' = Ar in the following forms. A. In eigenvalue/eigenvector form: [x] = ₁ C1 ]+[ ]). 3. In fundamental matrix form: [x]- C. As two equations: (write "c1" and "c2" for c₁ and c₂) x(t) = y(t) = []

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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Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: À = 2 with eigenvector = [] a and generalized eigenvector i = [_] Write the solution to the linear system' = Ar in the following forms. A. In eigenvalue/eigenvector form: [x] = B1 [18-18). + B. In fundamental matrix form: x(1) = [a] C. As two equations: (write "c1" and "c2" for c₁ and c₂) x(t) = y(t) = Note: if you are feeling adventurous you could use other eigenvectors like 47 and other generalized eigenvectors like w - 3 v. Just remember that if you change , you must also change for its fundamental solution! C₁
Transcribed Image Text:Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: À = 2 with eigenvector = [] a and generalized eigenvector i = [_] Write the solution to the linear system' = Ar in the following forms. A. In eigenvalue/eigenvector form: [x] = B1 [18-18). + B. In fundamental matrix form: x(1) = [a] C. As two equations: (write "c1" and "c2" for c₁ and c₂) x(t) = y(t) = Note: if you are feeling adventurous you could use other eigenvectors like 47 and other generalized eigenvectors like w - 3 v. Just remember that if you change , you must also change for its fundamental solution! C₁
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