## Math 160 - Chapter 4 Study Guide

1. Find the inverses of a 2x2 and 3x3 matrix, if they exist. Two parts. Look at problems 4.5.29 - 4.5.42.
2. Solve the 3x3 system of linear equations. Be aware of the special case of no solution and be able to write the answer in parametric form. Three parts. Look at problems 4.3.25 - 4.3.44.
3. Write the solution to the system of linear equations from the augmented matrix. Three parts ... including the special cases.
4. Solve the equation for X. Three parts. Know how to handle factoring of matrices and scalar multiplication. Look at problems 4.6.31 - 4.6.36.
5. Break-even analysis. Two parts. Look at problems 4.1.47 - 4.1.50. You will be required to create the cost and revenue equations from the information in the problem.
6. Leontief Input-Output Analysis. Write the input-output matrix and find the output. Look at problems 4.7.23 - 4.7.28.
7. Traffic flow. Four parts. Look at problems 4.3.71 - 4.3.72.
8. Linear Algebra application of matrices. Find the volume of a parallelpiped. The formula is given. You have to be able to do some subtraction, enter matrices into calculator, find determinants, transposes, and products of matrices using the calculator.
9. Statistics. Two parts. Find the least squares regression parabola passing through the points given. This involves solving a matrix equation (similar to problem 4), and then plug the given matrices into the calculator to actually find the answer. For those who had me for College Algebra, take a look at problem 8 on the chapter 6 take home exam.
10. Incidence Matrix. Two parts. Look at problems 4.4.59 - 4.4.60.

### Notes:

• Problems 1 - 7 must be worked individually and turned in before getting into groups.
• Problems 8 - 10 may be worked in groups of up to three people. Submit one paper for each person.

Breakdown of points by problem.

 1 2 3 4 5 6 7 8 9 10 Total 8 12 9 12 8 10 10 15 8 8 100