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- A school district has 3 high schools. At the end of each year,
teachers can be moved from one school to another. The picture below depicts
the probability that a teacher will move from one school to another this
year.
- Construct and label the transition matrix that corresponds to this picture. Name the matrix A.
- If a teacher works in school A this year, what is the probability that he or she will work in school C next year?
- If a teacher works in school C this year, what is the probability that he
or she will work in school B in the year after next (i.e., 2 years
from now)?
- Matrix A is the transition matrix for one year. Find the transition
matrix for two years.
- Find the transition matrix for three years.
- Find, to two decimal places, the matrix to which A appears to converge after many years.
- Explain the meaning of your solution to problem 1f.
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- Using the following data and the normal equation, find the "best
fit" straight line, accurate to one decimal place, to the points.
- Using the following data and the normal equation, find the "best
fit" straight line, accurate to one decimal place, to the points.
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- Using the following data and the normal equation, find the "best
fit" parabola, accurate to one decimal place, to the points.
- Using the following data and the normal equation, find the "best fit" parabola, accurate to one decimal place, to the points.
- Use the power method to find the dominant eigenpair of the matrix A
from problem 1.
- Use the power method to find the dominant eigenpair of the matrix
- Use the characteristic equation to find both of the eigenpairs of the
matrix
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