# Finite Projects

Listed below are the various projects that will be required throughout the semester. Each of these are worth 25 points and will be due the day following the exam for the appropriate chapter. These projects take you above and beyond the material covered in the book or require outside data acquisition. You may work in groups of up to three people per project. Turn in one project with all group member's names on it. Plan on reading the section of the book dealing with the matter before we cover it in class; you will not always have time to finish the project if you wait until we do. Give me the results of any surveys along with the projects.

### Project 1, Chapter 4

Identify a car or other object of more than \$5000 which you would like to purchase. This can come from a television, radio, or newspaper ad, or a dealer. Contact your bank or credit union to find the current interest rates. In your project, identify the object you wish to purchase and the list price. Then, compute and give the monthly payments, total payment, and amount of interest on the object for 36, 48, and 60 months loan. Use the interest rate given by your lending institution and also 2.9% and 12.9%. Note there will be nine groups here (3 different months by 3 different rates).

### Project 2, Chapter 5

Use the matrices A,B,C,O,D and I given on the handout to verify the properties below.

4. Associativity of multiplication
5. Identity for multiplication
6. Left distributive
7. Right distributive
8. Transpose of the transpose
9. Transpose of a sum
10. Transpose of a product
11. Determinant of product
12. Determinant of transpose
13. Inverse of a product
14. Examine Det D and explain why D has no inverse. Then, row-reduce the augmented matrix and explain what happens when a matrix has no inverse.

### Project 3, Chapter 7

Create a fair game for two or more players with at least four distinct outcomes (this is easier with die/dice or a spinner). Create a payoff table (probability distribution).

### Project 4, Chapter 8

Pick a subject (mathematics, english, biology, etc). Ask at least 25 students "Did you have a 'math' class last semester?" and "Do you have a 'math' class this semester?". Using this semester's probabilities as a starting point, write the initial-state matrix and transition matrix. Find the next three state matrices and the steady-state matrix. Use the current state as the initial-state matrix.

Last updated: Saturday, June 10, 1995 at 3:26 pm