Unformatted text preview: stable distribution p: Ap=p or (AI)p=0 (*) First find the general family of solutions to (*), and then find the solutions that is a probability vector. A= ² ³ ³ ³ ³ ´ 1/3 2/3 2/3 1/6 2/3 1/6 1/6 1/6 1/6 1/6 1/6 2/3 1/6 2/3 2/3 1/3 µ ¶ ¶ ¶ ¶ · (10 points) 4. Consider the following growth model for elephants and mice: E’ = E  M M’=2E+4M a) Determine the eigenvalues of the coefficient matrix. (10 points) b) Determine the associated eigenvectors. (10 points) c) Write the coefficient matrix in the diagonalized form UD λ U1 . (5 points) 5. a) Find the condition number (with respect to the sum norm) of the coefficient matrix for the system of equations: (10 points) x y= 1 2x+4y=1 b) Give a bound on the relative error (percentage error) in the solution if the coefficient 4 in the second equation is erroneously entered as 3. (5 points)...
View
Full
Document
This note was uploaded on 08/08/2010 for the course AMS 210 taught by Professor Fried during the Spring '08 term at SUNY Stony Brook.
 Spring '08
 FRIED

Click to edit the document details