(This exercise builds on Exercise 101.) Consider) n x n matrix A whose entries are
Chapter 2, Problem 102(choose chapter or problem)
(This exercise builds on Exercise 101.) Consider) n x n matrix A whose entries are positive or zero. Su pose that all column sums of A are less than 1. Let r \ the largest column sum of A. a. Show that the entries of Am are less than or equal J rm, for all positive integers m.b. Show thatlim Am = 0 m>oo(meaning that all entries of Am approach zero), c. Show that the infinite series/ + A + A2 + + Am + converges (entry by entry).
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