Math 140: Unit 9

Due Date: Wednesday, December 4, 2002

Topics

The material in unit 10 is much different than in most of the other units. In this unit, instead of working primarily with functions, you will study systems of equations. We studied small (2x2) systems of linear equations briefly in section 1.2. These small linear systems are easy to solve via the substitution method, but that method is very poor for larger systems. So in this unit you will learn how to solve linear systems using the elimination method (the proper name is Gauss-Jordan Elimination). Systems of linear equations arise in many applications in many fields, and also in many areas of mathematics, so solving such systems is an important skill to learn. Therefore, no calculator is allowed for Unit 9.

• Systems of Linear Equations: Two equations in two variables (10.1)
  • Solve by substitution
  • Solve by elimination
  • Inconsistent systems
  • Dependent systems
  • Number of solutions
  • Applications
    
    
• Systems of Linear Equations: Three equations in three variables (10.2)
  • Solving three equations in three variables
  • Identify inconsistent systems
  • Solving a system of dependent equations
    
    
• Systems of Linear Equations: Matrices (10.3)
  • Matrices
    • Augmented matrix of a system
    • Reduced row echelon form
  • Elimination method using augmented matrices

Study guidelines

• Section 10.1 : Systems of Linear Equations: Two equations in two variables
  • Review the Section 1.3 and Appendix A.5 before you begin this section.
  • Read Section 10.1.
  • You should be ale to solve systems of two equations in two variables and identify those systems that are inconsistent.
  • Study the applications.
  • Problems: 10.1 #22, 3, 11, 15, 17, 21, 29, 43, 45, 47, 51.
    
    
• Section 10.2 : Systems of Linear Equations: Three equations in three variables
  • Read Section 10.2.
  • You should be ale to solve systems of three equations in three variables and identify those systems that are inconsistent.
  • Problems: 10.2 #1, 3, 7, 9, 11, 15.
  • Problems in applications (Ex. 17-27) will be covered in Unit 10.
    
    
• Section 10.3: Systems of Linear Equations: Matrices
  • Read Section 10.3.
  • You will learn how to use the augmented matrices to solve systems of three equations in three variables..
  • Problems: 10.3 # 3, 7, 9, 15, 17, 23, 25, 27, 33, 37, 45, 47, 50, 61.
  • Problems in applications (Ex. 69-87) will be covered in Unit 10.
    
    
• Supplementary material (optional) for Chapter 10:
  • Student Solutions Manual for Chapter 10(see note)
  • Video lectures are available in the Media Reserve room of the ISU library. They are listed under Math 140: Poon.
  • For tutoring help, visit the Prentice Hall Tutor Center. Tutors can be contacted by phone, fax, or e-mail. To register, you will need the access code that came with your textbook.
  • Graphing Calculator Help
  • The MathPak5 web site contains other resources such as Reading Quizzes and links to other interesting and fun math sites.

Unit Exam #9
After completing the above work, do the following:

1. Read the exam description:
   • No calculator is allowed for Unit 9.
   • This exam has 12 questions, and will count 15 points toward your grade.
   • The exam has a one hour time limit.
   • Remember that application problems from sections 10.2-10.3 will be covered in Unit 10.
   • Be sure to look under the entry box for the expected format of the answer.
     • Some problems require you to enter the augmented matrix of a system. There will be a blank for each entry of the matrix, and you can move between blanks using the TAB key or your mouse. However, note that there will be no vertical line between the last two columns in these particular problems.
2. Complete the online Unit 9 Pretest assignment. You may use your book if you wish, and redo the pretest as many times as you like. Your pretest score will be scaled to 5 points maximum.
3. You can repeat the online Unit 9 Pretest assignment without using your book until you feel that you are ready for the unit exam.
4. If you are having trouble with any of the problems listed above or on the pretest or practice exams, spend some time working with the online tutors listed on the Help page.
5. Go to the Math Computer Lab (449 Carver) to take the online proctored unit exam (go to Unit 9 Exam). Remember to bring identification, and remember that you will not be able to take the unit exam after the deadline date given at the top of this page. You may NOT use your book or notes on this exam.

   Note: Remember that you can always go back and take practice exams (go to Unit 9 Practice Exam) on this unit after the deadline has passed. In particular, this will help you prepare for the midterm and final exams.

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