Refer to the matrices P and Q of Problem 59. For k a positive integer, let Tk = I + Q + Q2 + ˆ™ ˆ™ ˆ™ + Qk.
(A) Explain why Tk+1 = TkQ + I.
(B) Using a graphing calculator and part (A) to quickly compute the matrices Tk, discover and describe the connection between (I - Q)-l and Tk when k is large.
Matrices of Problem 59

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0% D0423 C0136 B0351 A1200 ABCD