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3. (a) Diagonalize the matrix 4-(-3). A = i.e. write A = VAV-1, where V is the matrix whose colums are the eigenvectors of A, and A is the diagonal matrix with the eigenvalues of A on the diagonal. (b) Calculate et for the matrix in part (a). (c) Use your answer to (b) to solve the linear system using the formula 1 1 x = ( ² ) x + (1) ₁ y y (9). 5 -3 y(t) = e^ly (0) + * e^(t-s)q(s) ds.

3. (a) Diagonalize the matrix 4-(-3). A = i.e. write A = VAV-1, where V is the matrix whose colums are the eigenvectors of A, and A is the diagonal matrix with the eigenvalues of A on the diagonal. (b) Calculate et for the matrix in part (a). (c) Use your answer to (b) to solve the linear system using the formula 1 1 x = ( ² ) x + (1) ₁ y y (9). 5 -3 y(t) = e^ly (0) + * e^(t-s)q(s) ds.

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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3. (a) Diagonalize the matrix 4-(-3). A = i.e. write A VAV-¹, where V is the matrix whose colums are the eigenvectors of A, and A is the diagonal matrix with the eigenvalues of A on the diagonal. (b) Calculate eAt for the matrix in part (a). (c) Use your answer to (b) to solve the linear system using the formula x = ( ²3 ) x + (19). y y y(t) = e¹ty (0) + e^(-)q(s) ds.
Transcribed Image Text:3. (a) Diagonalize the matrix 4-(-3). A = i.e. write A VAV-¹, where V is the matrix whose colums are the eigenvectors of A, and A is the diagonal matrix with the eigenvalues of A on the diagonal. (b) Calculate eAt for the matrix in part (a). (c) Use your answer to (b) to solve the linear system using the formula x = ( ²3 ) x + (19). y y y(t) = e¹ty (0) + e^(-)q(s) ds.
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