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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.
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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)
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 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-