Question

2. 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:

I don't know what is the right answer