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Homework_9

# Homework_9 - Homework 9 Due Wed Nov 9th Math 224 Fall 2011...

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Homework 9 - Due Wed. Nov. 9th Math 224 - Fall 2011 Dr. Mauro Maggioni Office hours : Tue 4-5, in office 293 Physics Bldg. Phone : 660-2825 Web page : www.math.duke.edu/˜ mauro E-mail : mauro.maggioni at duke.edu Homework policies : as in homework 1. All the materials (code, figures, etc...) have to be turned in (as printouts!) with your homework, or the homework will not be graded. Assignment Study Lectures 22,22,24,25 in the book. Exercises 24.1. The following are taken from M. Heath Scientific Computing : True or false (prove your statements!) If a linear system is well-conditioned, then pivoting is unnecessary in Gaussian elimination. If a triangular matrix has a zero entry on its main diagonal, then the matrix is singular. If a matrix has a zero entry on its main diagonal, then the matrix is singular. If a matrix A is singular, then it does not have a full set of n linearly independent eigenvectors Given any arbitrary square matrix, there is some triangular matrix that is unitarily similar to it. Which of the following conditions necessarily imply that an

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