Suppose that A = S_S1, where _ is a diagonal matrix with diagonal elements 1, 2, . . .

Chapter 4, Problem 8

(choose chapter or problem)

Suppose that A = S_S1, where _ is a diagonal matrix with diagonal elements 1, 2, . . . , n. (a) Show that Asi = i si , i = 1, . . . , n. (b) Show that if x = 1s1+2s2+ +nsn, then Akx = 1k 1s1 + 2k 2s2 + +nk nsn (c) Suppose that |i | < 1 for i = 1, . . . , n. What happens to Akx as k ? Explain.

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