Applied Mathematics E2101yIntroduction to Applied MathematicsProblem Set #7, due Thursday, 9 April 2009All references are to Zill & Cullen (3rd edition).Chapter 8,§8.8: The Linear Eigenvalue Problem5122327 [You do not need to submit the logs of any computer experiments, but you are welcometo perform those indicated on your own in order to arrive at a conjecture about the leadingeigenvalue and its associated eigenvector for matrices whose row sum is one and all of whoseelements are nonnegative. You should submit your conjecture, and show why it is true witha simple matrix-vector multiplication, a one-line proof.]Chapter 8,§8.9: Powers of Matrices1715Chapter 8,§8.10: Orthogonal Matrices215Chapter 8,§8.11: Eigenvalue Approximation
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