Question: 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
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
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and let the initial distribution be
![.5 5]o](https://dsd5zvtm8ll6.cloudfront.net/si.question.images/image/images16/1385-M-S-L-P(2888)-2.png){kind=small}
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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