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Unformatted text preview: COT4501 Spring 2012 Homework IV Solutions Problem 1 1. FALSE. for example following matrix has only one real eigenvalue. A = 2 1- 1 1 1 1 1 1 2 , 2. False 3. For a given matrix • True • False 4. Which of the following conditions necessarily imply that a n × n real matrix A is diagonalizable (i.e., is similar to a diagonal matrix)? • A hasndistinct eigenvalues.——TRUE • A has only real eigenvalues.——-FALSE: needs to be distinct • A is nonsingular.—–FALSE: eigenvectors might not be linearly independent • A is equal to its transpose.——-TRUE • A commutes with its transpose.—–TRUE: makes it Normal matrix Problem 2 Is there any real value for the parameter α such that the matrix A = 1 α 4 2 6 5 3 , 1. Has all real eigenvalues? 2. Has all complex eigenvalues with nonzero imaginary parts? In each case, either give such a value for α or give a reason why none exists....
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- Spring '08
- Linear Algebra, Characteristic polynomial, Complex number, probability distribution vector