Final2008spring - Final Examination Spring 2008 Dierential...

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Final Examination - Spring, 2008. Differential Equations/Linear Algebra MTH 2201 05/02/2008 Time: 2 hours Max.Credit: 60 Answer all the questions. Make your answers precise and write legibly. Calculators are NOT allowed. 1. (a) Find the Laplace transform of the function f ( t ) = e t cos t . [5] (b) Find the inverse Laplace transform of F ( s ) = 1 s ( s 2 - 2 s +2) [5] (c) Use the Laplace transform to solve the initial value problem y - y = e t cos t, y (0) = 0 , y (0) = 0 . [5] 2. (a) Find the eigenvalues and eigenvectors of the matrix A = 1 0 0 2 2 - 1 0 1 0 . (b) Use Gauss elimination method and solve the system of equations: - 2 k 1 - k 2 + k 3 = - 1 - k 2 + k 3 = 1 (c) Find the fundamental matrix for the system of differential equations: x = x y = 2 x + 2 y - z z
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