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Unformatted text preview: Explain why any two choices of a lead to matrices A that are similar (with the same Jordan form). 3 3 (22 pts.) Suppose the 3 by 3 matrix A has independent eigenvectors in Ax 1 = 1 x 1 , Ax 2 = 2 x 2 , Ax 3 = 3 x 3 . (Those s might not be dierent.) (a) (11 points) Describe the general form of every solution u ( t ) to the dierential equation du = Au . (The answer e At u (0) does not use the dt s and x s.) (b) (11 points) Starting from any vector u 0 in R 3 , suppose u k +1 = Au k . What are the conditions on the x s and s to guarantee that u k (as k ) ? Why ? 4...
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This note was uploaded on 01/14/2011 for the course EECS 18.06 taught by Professor Strang during the Spring '05 term at University of Michigan.
 Spring '05
 Strang

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