Unformatted text preview: (e) Show that no values of a and b lead to a system that has a proper node. 2. Three solutions of the equation x = Ax are @ e t + e 2 t e 2 t 1 A ; @ e t + e 3 t e 3 t e 3 t 1 A and @ e t ± e 3 t ± e 3 t ± e 3 t 1 A : Find the eigenvalues and eigenvectors of A : 3. Let &; ±; ²; and ³ be constant real numbers and A = @ ³ 1 ³ 1 ³ 1 A : a. Prove that e tA = @ 1 t 1 2 t 2 1 t 1 1 A : b. Use e tA to solve the initial value problem x = Ax ; x (0) = @ & ± ² 1 A : 1...
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 Spring '11
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 Math, Constant of integration, Boundary value problem, Eigenvalue, eigenvector and eigenspace, Orthogonal matrix, pdf document attachment

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