1. Consider the matrices of Exercise 47. Beginning with the initial distribution matrix, generate 10 more distributions. Continue to generate 10 more. The matrices will get closer and closer to a certain 2 × 1 matrix. What is that matrix?
Refer to Exercise 47,
Let A be the stochastic matrix

and let the initial distribution be

2. Repeat Exercise 49 for the matrices of Exercise 48.
3. Generate 35 successive powers of the matrix A from Exercise 47. (With a graphing calculator, the instruction [A]*Ans can be used to compute successive powers of a square matrix.) The matrices will get closer and closer to a certain 2 × 2 matrix. What is that matrix? How is that matrix related to the 2 × 1 matrix found in Exercise 49?
4. Repeat Exercise 51 for the square matrix of Exercise 48.

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