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la_m1_handouts - MAC 2103 Module 1 Systems of Linear...

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1 1 MAC 2103 Module 1 Systems of Linear Equations and Matrices I 2 Rev.F09 Learning Objectives Upon completing this module, you should be able to: 1. Represent a system of linear equations as an augmented matrix. 2. Identify whether the matrix is in row-echelon form, reduced row-echelon form, both, or neither. 3. Solve systems of linear equations by using the Gaussian elimination and Gauss-Jordan elimination methods. 4. Perform matrix operations of addition, subtraction, multiplication, and multiplication by a scalar. 5. Find the transpose and the trace of a matrix. http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
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2 3 Rev.09 Systems of Linear Equations and Matrices I http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Introduction to Systems of Linear Equations Introduction to Systems of Linear Equations Gaussian Elimination Gaussian Elimination Matrices and Matrix Operations Matrices and Matrix Operations There are three major topics in this module: 4 Rev.F09 A Quick Review http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. 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 0. 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.
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3 5 Rev.F09 http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Let’s Look at a System of Two Linear Equations in Two Variables 6 Rev.F09 http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Remember How to Use the Elimination Method 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, state whether the equations are dependent or independent . Support your results graphically. a) 3 x y = 7 b) 5 x y = 8 c) x y = 5 5 x + y = 9 5 x + y = 8 x y = 2
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4 7 Rev.F09 http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Solving a System of Linear Equations Using the Elimination Method (Cont.) Solution a) Eliminate Eliminate y y by adding by adding the equations. Find y by substituting x = 2 in either equation. The solution is ( 2 , 1 ). The system is consistent and the equations are independent . 8 Rev.F09 http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Solving a System of Linear Equations Using the
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This note was uploaded on 10/18/2011 for the course MAS 2103 taught by Professor Shaw during the Summer '11 term at Valencia.

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la_m1_handouts - MAC 2103 Module 1 Systems of Linear...

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