hello, feel free to use matlab, thank you

Markov Chains can be used by city planners to analyze trends in land use. 5 land uses are defined, and the element (i, j) of the transition matrix is the probability that the land that was in use / will be in use i 5 years later. For an imaginary city, the transition matrix and the key are presented below: 2 3 4 5 1. Residential 0.40 0.15 0.10 0.05 0.10 2. Offices 0.10 0.35 0.30 0.25 0.10 3. Commercial 0.15 0.15 0.50 0.10 0.40 4. Parking 0.10 0.30 0.10 0.40 0.20 5. Vacant 0.25 0.05 0 0.20 0.20I a) If the probability of use in the city in 2020 is [0.30 0.25 0.15 0.2 0.10] what would be the probability of land in the city to be vacant in 2030? b) In the long range, what would the probability of the land in the city to be used for parking or to be vacant? What does it tell us about the life of the city? c) Why do you think that the diagonal entries of the transition matrix are relatively large corresponding to the others? What does it mean about land use? d) There is a city-wide movement to monitor and increase the amount of green space in the city, and to allow for mixed-use of land (for example buildings that have parking underground, commercial use on the first floor, offices on the second floor, and apartments on the third to seventh floor). The non-profit A Better City (ABC) needs help to quantify this vision and you have been hired to help. Reorganize the land-use categories and the transition matrix for these new categories (many solutions are possible). Explain your reorganization, taking a group of columns in the initial matrix and the initial vector use as examples. c) For the new matrix you have proposed at point d, what would the probability of the land in the city to be used in the long range for parking or to be vacant? What does it tell us about the life of the city