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Unformatted text preview: Chapter1 Chapter1 Systems of Linear Equations and Systems of Linear Equations and atrices I atrices I Matrices I Matrices I Learning Objectives Learning Objectives Upon completing this Module, you should be able to: y Represent a system of linear equations as an p y q augmented matrix. y Identify whether the matrix is in rowechelon form, duced row helon form, both, or neither. reduced row echelon form, both, or neither. y Solve systems of linear equations by using the Gaussian elimination and GaussJordan elimination ethods. methods. y Perform matrix operations of addition, subtraction, multiplication, and multiplication by a scalar. y Find the transpose and the trace of a matrix. Systems of Linear Equations Systems of Linear Equations d Matrices d Matrices and Matrices and Matrices There are three major topics in this Module: y Introduction to Systems of Linear Equations y Gaussian Elimination y Matrices and Matrix Operations A Quick Review A Quick Review y A linear equation in two variables can be written in the form ax + by = k , where a , b , and k are constants, and a and b are not equal to . Note : The power of the variables is always 1 . Two or more linear equations is called a system of linear equations because they involve solving more than one linear equation at once. A system of linear equations can have either exactly one solution (unique), no solution, or infinitely many solutions. Lets Look at a System of Two Linear Equations Lets Look at a System of Two Linear Equations in Two Variables in Two Variables Possible Graphs of a System of Two Linear Equations in Two Variables How to Use the Elimination Method How to Use the Elimination Method Solve a System of Linear Equations? Solve a System of Linear Equations? to Solve a System of Linear Equations? to Solve a System of Linear Equations? Example: Use elimination to solve each system of equations , if possible. Identify the system as consistent or inconsistent. If the system is consistent, support your results graphically. Solving a System of Linear Equations Using the Solving a System of Linear Equations Using the Elimination Method (Cont.) Elimination Method (Cont.) ( ) ( ) liminate y adding Solution: Eliminate y by adding the equations. Find y by substituting x = 2 in either equation....
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 Spring '12
 alix

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