# Chapter 5: Study Guide

1. Solve a 2x2 system of linear equations. Look at problems 41 - 46 in section 5.1.
2. Leontief Input-Output Model. Look at problems 17 - 22 in section 5.8.
3. Work a problem using an incidence matrix. Similar to the air freight problems 47 - 49 in section 5.5. Six parts.
4. Traffic Flow. Look at problems 67 - 68 in section 5.3. The diagram is given, but the variables aren't identified. You will need to identify the variables and set up the equations. Then solve the equations and label the diagram with the correct traffic flow rates. Determine the maximum and minimum values for a certain route, and then identify traffic flow for a specific rate. Four parts.
5. Solve a system of linear equations. Look at problems 37 - 42 in section 5.7.
6. List the three elementary row operations.
7. List the four requirements of being in reduced row-echelon form.
9. Multiply a scalar and a matrix.
10. Multiply two matrices.
11. Find the inverse of a 2x2 matrix.
12. Find the inverse of a 5x5 blocked matrix.
13. Find the transpose of a matrix.
14. Find the determinant of a matrix.
15. Raise a matrix to a power.
16. Multiply a matrix by the inverse of the matrix.
17. Solve a matrix equation for X. Three parts.
18. True or False. Seven questions about properties of matrices. Reading through the properties of matrices that are in the text will be beneficial. Also, as a way to test each statement, create two matrices on the calculator. Make sure they are not symmetric. If the property works, it probably is true, but if it doesn't work, then it definitely is false.

You may work this exam with a partner. The first 40 minutes of the exam will be individually worked. Then, you may get together for the last 20 minutes. Work as many of the problems as you can, productivity goes down when you start arguing answers.

Last updated: Thursday, June 20, 1996 at 6:49 AM