Where row 1 shows how the metropolitan population M changed (80% remained in Mto S) and row 2 shows how the population of the surrounding çountieschanged. Currently, the population is evenly divided between the two areas, which can beand 20% movedrepresented by the row matrix.P = [% in M % in S] = [50% 50%] = [0.5 0.5]%3D%3D%3Da) Form the product PD and interpret its entries.b) Prediction of this population distribution after 10 years and after 15 years could be foundfrom what matrix products? Suppose that for a certain metropolitan area and the surrounding counties during each 5year period, an average of 20% of the metropolitan population M moves to thesurrounding counties and the rest remains. Similarly, suppose that in the same period,an average of 30% of the surrounding counties' population S moves to the metropolitanarea and the rest remains. This population dynamic can be represented as the matrix[80% 20%[30% 70%[0.8 0.21L0.3 0.7]D%3D

The population dynamic is represented as D=0.80.20.30.7 and the population matrix is P=0.50.5. a)…

Answered: a) Form the product PD and interpret…

a) Form the product PD and interpret its entries. b) Prediction of this population distribution after 10 years and after 15 years could be found from what matrix products?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

Where row 1 shows how the metropolitan population M changed (80% remained in M
to S) and row 2 shows how the population of the surrounding çounties
changed. Currently, the population is evenly divided between the two areas, which can be
and 20% moved
represented by the row matrix.
P = [% in M % in S] = [50% 50%] = [0.5 0.5]
%3D
%3D
%3D
a) Form the product PD and interpret its entries.
b) Prediction of this population distribution after 10 years and after 15 years could be found
from what matrix products?

Suppose that for a certain metropolitan area and the surrounding counties during each 5
year period, an average of 20% of the metropolitan population M moves to the
surrounding counties and the rest remains. Similarly, suppose that in the same period,
an average of 30% of the surrounding counties' population S moves to the metropolitan
area and the rest remains. This population dynamic can be represented as the matrix
[80% 20%
[30% 70%
[0.8 0.21
L0.3 0.7]
D
%3D

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