## Math 160 - Chapter 4 Study Guide

- Find the inverses of a 2x2 and 3x3 matrix, if they exist. Two parts. Look at problems 4.5.25 -
4.5.38*.
- 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 4.3.23 - 4.3.42*.
- Solve the equation for X. Two parts. Know how to handle factoring of matrices and scalar
multiplication. Look at problems 4.6.21 - 4.6.26.
- Break-even analysis. Two parts. Look at problems 4.1.51 - 4.1.54. You will be required to
create the cost and revenue equations from the information in the problem.
- Leontief Input-Output Analysis. Four parts. Look at problems 4.7.23 - 4.7.28*.
- Traffic flow. Four parts. Look at problems 4.3.71 - 4.3.72.
- Statistics. Two parts. Find the least squares regression parabola passing through the points
given. This involves solving a matrix equation (similar to problem 6), and then plug the given
matrices into the calculator to actually find the answer.
- Incidence Matrix. Two parts. Look at problems 4.4.61 - 4.4.62.

### Notes:

- Starred (*) problems are directly from the textbook, but may be even or odd.
- Problems 1 - 5 must be worked individually and turned in before getting into groups.
- Problems 6 - 8 may be worked in groups of up to three people.

Breakdown of points by problem.

1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
Total |

10 |
15 |
10 |
15 |
15 |
15 |
10 |
10 |
100 |