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Unformatted text preview: MA366 Final Last Name: First Name: Show all work. A correct answer without supporting work is worth NO credit! (Some calculators can solve differential equations.) There should be no hard integrals, unless you mess up somewhere. If this happens, just leave it as an integral and explain how to finish the problem. 1 2 (1) The following vectors X 1 and Y 1 are eigenvectors for a certain 3 3 matrix A corresponding to the eigenvalues 2 i and 4 respectively. Find the general solution to the system X = AX in real form . No complex numbers allowed! 5 pts. x 1 = i + 1 i 2 i , y 1 = 1 3 1 . 3 (2) The characteristic polynomial for the following matrix is p ( r ) = ( r 4) 2 ( r 5) and the vector Y 1 is an eigenvector corre sponding to r = 5. Find the general solution to the system X = AX . 10 pts. 7 0 1 4 2 0 6 3 4 Y 1 =  3 4 6 4 (3) Given that X 1 , X 2 and X 3 are eigenvectors for the following matrix, find the general solution to...
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 Spring '08
 CHO
 Equations, Integrals

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