Answered: In 2009, the population of the U.S.,…

Name: In 2009, the population of the U.S., broken down by regions, was 54.6
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Description: In 2009, the population of the U.S., broken down by regions, was 54.6 million in the Northeast, 66.0 million in the Midwest, 111.8 million in the South, and 70.6 million in the West. The table below shows the population movement during the period 200

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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In 2009, the population of the U.S., broken down by regions, was 54.6 million in the Northeast, 66.0 million in the Midwest, 111.8 million in the South, and 70.6 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

Use matrix inversion and multiplication to estimate the population in each region in 2008. (Round all answers to the nearest 0.1 million.)

SEE PICTURE!!!

**U.S. Population Analysis and Movement (2008-2009)**

In 2009, the population of the U.S., broken down by regions, was:
- 54.6 million in the Northeast
- 66.0 million in the Midwest
- 111.8 million in the South
- 70.6 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).

### Population Movement Table

| | To Northeast | To Midwest | To South | To West |
|--------|--------------|------------|----------|---------|
| **From Northeast** | 0.9923 | 0.0016 | 0.0042 | 0.0019 |
| **From Midwest** | 0.0018 | 0.9896 | 0.0047 | 0.0039 |
| **From South** | 0.0021 | 0.0059 | 0.9827 | 0.0085 |
| **From West** | 0.0024 | 0.0033 | 0.0038 | 0.9905 |

### Instructions

**1. Set Up the 2009 Population Figures as a Row Vector:**
(Enter your answers in millions.)

\[ \begin{pmatrix}
54.6 & 66.0 & 111.8 & 70.6
\end{pmatrix} \]

**2. Use Matrix Inversion and Multiplication to Estimate the Population in Each Region in 2008:**
(Round all answers to the nearest 0.1 million.)

| Region | Population (in millions) |
|-----------|-----------------------------|
| Northeast | [input field] |
| Midwest | [input field] |
| South | [input field] |
| West | [input field] |

*Need Help?* [Read It]

---

### Explanation of Diagrams

1. **Population Movement Table:**
This table illustrates the percentage of the population that stayed in their original region or migrated to another region from 2008 to 2009. It is crucial for understanding regional demographic shifts

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