# Section 16.6: Review for Chapter 16

Studying for a chapter examination is a personal process, one which nobody else can do for you. Simply take the time to review what you have done.

Here are the new terms in Chapter 16.

Array [16.3]
Associative property [16.4]
Augmented matrix [16.3]
Column [16.3]
Communication matrix [16.4]
Commutative property [16.4]
Constraint [16.5]
Convex set [16.5]
Demand [16.2]
Demand curve [16.2]
Dependent system [16.1]
Diagonal form [16.3]
Dimension [16.3]
Distributive property [16.4]
Double subscripts [16.3]
Elementary row operations [16.3]
Equal matrices [16.4]
Equilibrium point [16.2]
Equivalent matrices [16.3]
Equivalent systems [16.1]
Feasible solution [16.5]
Gauss-Jordan elimination [16.3]
Graphing method [16.1]
Identity matrix [16.4]
Inconsistent system [16.1]
Inverse matrix [16.4]
Inverse property [16.4]
Linear combination method [16.1]
Linear programming [16.5]
Linear system [16.1]
Main diagonal [16.4]
Matrix [16.3]
Matrix equation [16.3, 16.4]
Multiplication of matrices [16.4]
Multiplicative inverse [16.4]
Nonconformable matrices [16.4]
Nonsingular matrix [16.4]
Objective function [16.5]
Optimum solution [16.5]
Order [16.3]
Pivot [16.3]
Pivot row [16.3]
Pivoting [16.3]
Row [16.3]
Row+ [16.3]
Row-reduced form [16.3]
RowSwap [16.3]
Scalar [16.3]
Scalar multiplication [16.4]
Simultaneous solution [16.1]
Singular matrix [16.4]
Square matrix [16.3]
Subscript [16.3]
Substitution method [16.1]
Subtraction of matrices [16.4]
Superfluous constraint [16.5]
Supply [16.2]
Supply curve [16.2]
System of equations [16.1]
System of inequalities [16.5]
Target row [16.3]
*Row [16.3]
*Row+ [16.3]
Zero matrix [16.4]

If you can describe the term, read on to the next one; if you cannot, then look it up in the text (the section number is shown in brackets).

IMPORTANT IDEAS

Can you explain each of these important ideas in your own words?

Systems of equations (graphing, substitution, and addition) [16.1]
Four elementary row operations [16.3]
Process of pivoting [16.3]
Gauss-Jordan elimination [16.3]
Matrix operations [16.4]
Properties of matrices [16.4]
Inverse of a matrix [16.4]
Systems of inequalities [16.5]
Linear programming theorem [16.5]

Next, make sure you understand the types of problems in Chapter 16.

TYPES OF PROBLEMS

Solve systems of equations by graphing, substitution, or addition, as directed. [16.1]
Solve systems of equations by selecting the most appropriate method. [16.1]
Solve applied problems, including coin problems, combining rates, supply and demand, and
mixture problems. [16.2]
Know the relationship between a system of equations and a corresponding matrix [16.3]
Perform elementary row operations on a given matrix. [16.3]
Solve systems of equations by the Gauss-Jordan method. [16.3]
Carry out matrix operations, including finding the inverse of a given matrix. [16.4]
Solve a system of equations using the inverse matrix method. [16.4]
Solve a system of inequalities. [16.5]
Decide whether a given point is a feasible solution for a set of constraints. [16.5]
Decide whether a given point is a corner point for a set of constraints. [16.5]
Find the corner points for a set of feasible solutions. [16.5]
Maximize or minimize an objective function subject to a set of constraints. [16.5]
Solve applied problems using a linear programming model. [16.5]

Once again, see if you can verbalize (to yourself) how to do each of the listed types of problems. Work all of Chapter 16 Review Questions (whether they are assigned or not).

Work through all of the problems before looking at the answers, and then correct each of the problems. The entire solution is shown in the answer section at the back of the text. If you worked the problem correctly, move on to the next problem, but if you did not work it correctly (or you did not know what to do), look back in the chapter to study the procedure, or ask your instructor. Finally, go back over the homework problems you have been assigned. If you worked a problem correctly, move on the next problem, but if you missed it on your homework, then you should look back in the text or talk to your instructor about how to work the problem. If you follow these steps, you should be successful with your review of this chapter.

We give all of the answers to the Chapter Review questions (not just the odd-numbered questions), so be sure to check your work with the answers as you prepare for an examination.