Textbook Problem

Population Movement In 2008 the population of the United States, broken down by regions, was 54.1 million in the Northeast, 65.7 million in the Midwest, 112.9 million in the South, and 70.3 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.)¹⁵

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 as a row vector. Then use matrix multiplication to estimate the population in each region in 2009. (Round all answers to the nearest 0.1 million.)