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Unformatted text preview: Section 2.2 Solving Systems of Linear Equation I 1 Section 2.2 - Solving Systems of Linear Equations I As you may recall from College Algebra, you can solve a system of linear equations in two variables easily by applying the substitution or addition method. Since these methods become tedious when solving a large system of equations, a suitable technique for solving such systems of linear equations of any size is the Gauss-Jordan elimination method . This method involves a sequence of operations on a system of linear equations to obtain at each stage an equivalent system. The Gauss-Jordan elimination method is complete when the original system has been transformed so that it is in a certain standard form from which the solution can be easily read. Augmented Matrices Matrices are rectangular arrays of numbers. We will use these to solve systems of equation in 2 or more variables. Example: Given 2 2 27 5 8 3 22 6 4 2 = + +- = + + = + + z y x z y x z y x . The coefficient matrix is: - 2 1 1 5 8 3 6 4 2 . The augmented matrix is: - 2 27 22 | | | 2 1 1 5 8 3 6 4 2 Section 2.2 Solving Systems of Linear Equation I 2 Example: The augmented matrix is: -- 8 2 6 1 1 5 5 4 1 2 . Write down the system....
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