A second market research project also suggested that if the Westmall shopping centre were sold, each of the three centres (Westmall, Grandmall and Eastmall) would continue to have regular shoppers but would attract and lose shoppers on a weekly basis.
Let `R_n` be the state matrix that shows the expected number of shoppers at each of the three centres `n` weeks after Westmall is sold.
A matrix recurrence relation that generates values of `R_n` is
`R_(n+1) = TR_n + B`
`{:(quad qquad qquad qquad qquad qquad qquad qquad text(this week)),(qquad qquad qquad qquad qquad qquad quad \ W qquad quad G qquad quad \ E),(text(where)\ T = [(quad 0.78, 0.13, 0.10),(quad 0.12, 0.82, 0.10),(quad 0.10, 0.05, 0.80)]{:(W),(G),(E):}\ text(next week,) qquad qquad B = [(-400), (700), (500)]{:(W),(G),(E):}):}`
The matrix `R_2` is the state matrix that shows the expected number of shoppers at each of the three centres in the second week after Westmall is sold.
`R_2 = [(239\ 060), (250\ 840), (192\ 900)]{:(W),(G),(E):}`
- Determine the expected number of shoppers at Westmall in the third week after it is sold. (1 mark)
- Determine the expected number of shoppers at Westmall in the first week after it is sold. (1 mark)