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In 2012 the population of California was 38,041,430, and the population living in the United States but outside California was 275,872,610. During the year, it is estimated that 748,252 persons moved from California to elsewhere in the United States, while 493,641 persons moved to California from elsewhere in the United States.$^4$a. Set up the migration matrix for this situation, using five decimal places for the migration rates into and out of California. Let your work show how you produced the migration matrix.b. [M] Compute the projected populations in the year 2022 for California and elsewhere in the United States, assuming that the migration rates did not change during the 10-year period. (These calculations do not take into account births, deaths, or the substantial migration of persons into California and elsewhere in the United States from other countries.)

a. $\left[\begin{array}{cc}{0.98033} & {0.00179} \\ {0.01967} & {0.99821}\end{array}\right]$b. The population of California is estimated to be 35,729,000 and the population of the rest of the US is estimated to be 278,190,000.

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 10

Linear Models in Business, Science, and Engineering

Introduction to Matrices

Campbell University

Baylor University

Lectures

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So in this program, we are going to set Happy Jin said have a difference. Um, question by off finding out transition metrics. And so in this case, XK means he has to entrance the first entrance. The population in California and then a second transience the the population, you know elsewhere. So I will say the rest pot. And if we define the variable in this way, the transition matrix in has four engines. So the first intron will be the the rate of people stay in California. And this, in turn, will be the people the right off people left. So I was a leave Californian. So this is the first column. And for the second car in the first century will be the people. Um stay outside and the 2nd 1 will be the people. The rate of people moved to California. So? So if we switch the order in XK, we need to switch the order here too. But I first used this order, um, the tradition matrix. And because Teoh, um, their point is your one night ah, seven. And the 0.0 has your 0.9 aids. 03 So in 98 0 33 So should be if they use five off digit we will have on this is 1967 And for the second column, we have, um, your 0.179 and the 0.998 to what? Okay, So this is our churches, your metrics. And we are looking for X 20 6 20 calls to end times x 19 and recursive li equals to end times and times X to the 80. So in the end, we have entered 20 times, eg zero and the miss case x zero is given. Um, so you see, ex zero. Because to on this So we just use a calculator and that you will gives us, um, the result. The second screen I'm next year will be this. So just use a calculator in the in the end, we have the solution, x 20 x 20. So you should be extend north 20 x 10 equals Teoh. Um, this So this is a population in the California after 10 years. Since we reiterate this a recursive equation 10 times

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