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- An amateur meteorologist predicts the weather based solely on today's
weather. The picture below depicts the probability that the weather will
either be sunny, cloudy, or rainy based on the weather today.
- Construct and label the transition matrix that corresponds to this
picture. Name the matrix A.
- If the weather is rainy today, what is the probability that it will
be cloudy tomorrow?
- If it is sunny today, what is the probability that it will be cloudy
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 three decimal places, the matrix to which A
appears to converges 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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