Question

Suppose that the 2015 state of land use in a city of 100 mi2 of built-up area is C: Commercially used 25% I: Industry Used 20% R: Residentially used 45% S: Used for Sports and recreation 10% Here C, I, R and S are states. The usage of land will change from one state to another state for every 5 year time period. The following matrix A will represent the transition probabilities of use of land from one state to another state after 5 years. Find the land use % in the years 2025, 2030 and 2035. To C I R S C 0.6 0.1 0 0.1 A = From I 0.2 0.9 0.2 0.4 R 0.1 0 0.7 0.2 S 0.1 0 0.1 0.3 Note that A is a stochastic matrix , that is, a square matrix with all entries nonnegative and all column sums equal to 1. The land use % for various states in 2025 is given by X1=AX The land use % for various states in 2030 is given by X2=AX1 The land use % for various states in 2025 is given by X3=AX2 where T x= 0.25 0.2 0.45 0.1​

Answer 1

Answer:

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Explanation:

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