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Unformatted text preview: c Kendra Kilmer August 18, 2011 Section 2.2 - Systems of Linear Equations (The Gauss-Jordan Method) This method allows us to strategically solve systems of linear equations. We perform operations on an aug- mented matrix that is formed by combining the coefficient matrix and the constant matrix as shown in the next example. Example 1: Find the intial augmented matrix for the system of equations below: a) 2 x- 4 y = 10 y = 1- 3 x b) x 1- 2 x 2 = 10 x 3 + 5 8 x 2 = x 1- 3 x 3 4 x 1- 3 x 3 = x 2 The goal of the Gauss-Jordan Elimination Method is to get the augmented matrix into Row Reduced Form . A matrix is in Row Reduced Form when: 1. Each row of the coefficient matrix consisting entirely of zeros lies below any other row having nonzero entries. 2. The first nonzero entry in each row is 1 (called a leading 1) 3. In any two successive (nonzero) rows, the leading 1 in the lower row lies to the right of the leading 1 in the upper row....
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