# Math 160: Study Guide - Chapter 4

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 cases of no solution or many solutions 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. 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.
4. Solve the equation for X. Four 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. Incidence Matrix. Two parts. Look at problems 4.4.59 - 4.4.60.
8. Construct a mathematical model for problem and use the inverse of a matrix to find the solution. Look at problems 4.6.43-50.
9. 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.
10. 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.
11. 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 - 8 must be worked individually and turned in before getting into groups.
• Problems 9 - 11 may be worked in groups of up to three people. Submit one paper for each person.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 Total 8 12 12 12 8 8 8 8 12 6 6 100