## Math 160 - Chapter 4 Study Guide

- Find the inverses of a 2x2 and 3x3 matrix, if they exist. Two parts. Look at problems
4.5.29 - 4.5.42.
- Solve the 3x3 system of linear equations. Be aware of the special cases of no solution or
many solutions and be able to write the answer in parametric form. Four parts. Look at
problems 4.3.25 - 4.3.44.
- Write the solution to the system of linear equations from the augmented matrix. Four
parts ... including the special cases. The matrices may be in either row echelon form or
reduced row echelon form. Look at problems 4.3.11-18.
- 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.
- 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.
- Leontief Input-Output Analysis. Write the input-output matrix and find the output. Look
at problems 4.7.23 - 4.7.28.
- Incidence Matrix. Two parts. Look at problems 4.4.59 - 4.4.60.
- Traffic flow. Create and solve the system of linear equations necessary to find the
network flow. Give the limitations on the parameter. Find the traffic flow for a particular
value of the parameter. Look at problems 4.3.73 - 4.3.74.
- 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.
- 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.

### 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 |
12 |
9 |
8 |
10 |
8 |
14 |
10 |
9 |
100 |