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Unformatted text preview: Homework 2 Solution 1. Given A = 6 4 2 , the eigenvalues are Î» i = 6 , 2 and corresponding eigenvectors are v i = 1 , 1 1 . The general solution is Î¾ ( t ) = c 1 1 e 6 t + c 1 1 1 e 2 t Given Î¾ (0) = 2 1 = c 1 1 + c 2 1 1 , then c 1 = 1, c 2 = 1, and the solution is Î¾ ( t ) = 1 e 6 t + 1 1 e 2 t 2. Given A =  3 3 1 1 3 , the eigenvalues are Î» i = 4 , 3 , 2 and corresponding eigenvectors are v i =  1 1 , 1 , 1 1 . The general solution is Î¾ ( t ) = c 1  1 1 e 4 t + c 2 1 e 3 t + c 3 1 1 e 2 t Given Î¾ (0) = 3 2 2 = c 1...
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This homework help was uploaded on 04/20/2008 for the course AME 30315 taught by Professor Goodwine during the Spring '08 term at Notre Dame.
 Spring '08
 Goodwine

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