M235A4b - MATH 235 Diagonalization - 2 Assignment 4b Hand...

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Unformatted text preview: MATH 235 Diagonalization - 2 Assignment 4b Hand in questions 2,3,4,5,6,7,9 by 9:30 am on Wednesday October 25, 2006. 1. Find the eigenvalues and eigenvectors of A = 1 1 0 0 4 1 0 0 a 0 2 0 c b 2 . Is A diagonalizable? 2. Diagonalize, if possible, the following matrices: A = 1 0 1 0 1 0 1 0 1 , B = - 2 4 i 4 i- 4 i 2 4 i 2 . 3. A 3 3 real matrix A has eigenvalues 1 = 2 =- 2 , 3 = 3 and associated eigenvectors v 1 = 1 1 , v 2 = 1 1 , v 3 = 1 1 1 , respectively. Find A . 4. Consider the matrix: A = 0 2 0 0 k 0 2 0 k 0 2 0 0 k where k is a constant. (a) Find a value of k such that A is diagonalizable. (b) Find a value of k such that A is not diagonalizable. 5. For A = " 4- 6 3- 5 # , evaluate A n for arbitrary positive integer n ....
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This note was uploaded on 01/05/2012 for the course MATH 235 taught by Professor Celmin during the Fall '08 term at Waterloo.

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M235A4b - MATH 235 Diagonalization - 2 Assignment 4b Hand...

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