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Math 242 Exam 4 Study Guide: Definitions, Vocabulary, and Problem Solving - Prof. Mark D. , Exams of Pre-Calculus

A study guide for exam 4 of math 242. It includes definitions and vocabulary related to topics such as inconsistent and dependent systems, gaussian elimination, objective functions, and matrices. Students are expected to be able to solve various problems related to these topics, including systems of linear and nonlinear equations, inequalities, and linear programming problems. The guide also includes review problems and practice exercises.

Typology: Exams

Pre 2010

Uploaded on 08/19/2009

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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

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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- Chapter Test (p567): 2, 3, 5, 6, 9-18, 20, 21; (p637): 1-