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- A very mathematical young lady decides what type of clothes that she
will wear tomorrow based on what she wears today. The picture below depicts
the probability that she will wear jeans, slacks, or a dress tomorrow based on what she wears today.
- Construct and label the transition matrix that corresponds to this picture. Name the matrix A.
- If she wears jeans today, what is the probability that she will wear address tomorrow?
- If she wears a dress today, what is the probability that she will wear
slacks the day after tomorrow (ie., 2 days from now)?
- Matrix A is the transition matrix for one day. Find the transition matrix for two days.
- Find the transition matrix for three days.
- Find, to two decimal places, the matrix to which A appears to converge after many days.
- Explain the meaning of your solution to problem 1f.
- 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" parabola, accurate to one decimal place, to the points.
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- 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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