Population Movement In 2008 the population of a country, broken down by regions, was 54.3 million in the Northeast, 65.1 million in the Midwest, 112.9 million in the South, and 70.9 million in the West. The table below shows the population movement during the period 2008–2009. (Thus, 99.23% of the population in the Northeast stayed there, while 0.16% of the population in the Northeast moved to the Midwest, and so on.)ToNortheastMidwestSouthWestFromNortheast0.99230.00160.00420.0019Midwest0.00180.98960.00470.0039South0.00560.00590.98270.0058West0.00240.00330.00440.9899Set up the 2008 population figures (in millions) as a row vector. Use matrix multiplication to estimate the population in each region in 2009. (Round all answers to the nearest 0.1 million.)Northeast million peopleMidwest million peopleSouth million peopleWest million people

Answered: 5.1 million in the Midwest, 112.9…

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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Question

Population Movement In 2008 the population of a country, broken down by regions, was 54.3 million in the Northeast, 65.1 million in the Midwest, 112.9 million in the South, and 70.9 million in the West. The table below shows the population movement during the period 2008–2009. (Thus, 99.23% of the population in the Northeast stayed there, while 0.16% of the population in the Northeast moved to the Midwest, and so on.)

To	Northeast	Midwest	South	West
From	Northeast	0.9923	0.0016	0.0042	0.0019
Midwest	0.0018	0.9896	0.0047	0.0039
South	0.0056	0.0059	0.9827	0.0058
West	0.0024	0.0033	0.0044	0.9899

Set up the 2008 population figures (in millions) as a row vector.

Use matrix multiplication to estimate the population in each region in 2009. (Round all answers to the nearest 0.1 million.)

Northeast million peopleMidwest million peopleSouth million peopleWest million people

Expert Solution

Step 1

Matrix Multiplication:

Given two matrices A and B, the multiplication of matrix A by matrix B may be expressed as (AB). That is, the resulting matrix for multiplying any $m \times n$ matrix 'A' with an $n \times p$ matrix 'B' is a matrix 'C' of order $m \times p$ . In the following part, we'll go over this topic in further depth.