## 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. 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.
4. 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.
5. Leontief Input-Output Analysis. Look at problems 4.7.23 - 4.7.28.
6. Incidence Matrix. Two parts. Look at problems 4.4.59 - 4.4.60.
7. Traffic flow. Four parts. Look at problems 4.3.71 - 4.3.72.
8. Linear algebra: Follow the instructions to create a matrix and then apply the formula given to find the quantity asked for. Involves determinants and transposes of matrices.
9. Statistics: Two parts. Find the least squares regression parabola passing through the points given. This involves solving a matrix equation (similar to problem 3), and then plug the given matrices into the calculator to actually find the answer.

### Notes:

• Problems 1 - 6 must be worked individually and turned in before getting into groups.
• Problems 7 - 9 may be worked in groups of up to three people.
• There are very few problems, so each one is worth a lot of points.

Breakdown of points by problem.
 1 2 3 4 5 6 7 8 9 Total 8 18 12 10 12 12 12 8 8 100