Math 242 EXAM 4 STUDY GUIDE
DEFINITIONS AND VOCABULARY:
Inconsistent and dependent systems (p510)
Gaussian elimination (p521)
Objective function and constraints (p552)
Set of feasible solutions (p552)
Matrix (p572)
Square matrix (p572)
Augmented matrix (p573)
Coefficient matrix (p573)
Row-echelon and reduced row-echelon form (p576)
Equal matrices (p587)
Properties of matrix addition and scalar multiplication (p590)
Zero matrix (p591)
Properties of matrix multiplication (p594)
Identity matrix (p594)
YOU SHOULD BE ABLE TO:
Solve a system of nonlinear equations using substitution or graphically using your calculator
Solve a system of linear equations using Gaussian elimination and back-substitution
Identify an inconsistent or dependent system and be able to write the general solution for a dependent system
Sketch the solution set to an inequality or system of inequalities in two variables
Sketch the region of feasible solutions for a linear programming problem
Find the minimum and maximum values of an objective function using linear programming
Solve applications using linear programming
Find the augmented matrix and coefficient matrix for a system of equations
Write the system of equations represented by its augmented matrix
Use Gauss-Jordan reduction to solve a system of linear equations using elementary row operations on the
augmented matrix
Use the augmented matrix and the rref command to solve a system of equations by Gauss-Jordan reduction
Solve applications involving systems of equations
Set up and find the partial fraction decomposition for a rational expression
Perform operations with matrices (addition, subtraction, exponents, scalar multiplication and matrix
multiplication) by hand and using the calculator
REVIEW PROBLEMS:
Review Exercises (p563): 5-8, 11-14, 33-42, 49-60, 63-74, 77-86; (p632): 1-8, 25-66
Chapter Test (p567): 2, 3, 5, 6, 9-18, 20, 21; (p637): 1-4