14111cn2.6 - 2 The first nonzero entry in each row is...

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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.
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Unformatted text preview: 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. 4. If a column contains a leading 1, then the other entries in that column are zeros. Note: We only consider the coefficient side (left side) of the augmented matrix when determining whether the matrix is in row-reduced form. Example 2: Are the following in Row Reduced form? a) 1 0 0 0 1 0 0 0 1 3 b) 1 2 0 0 0 1 0 0 0 1 c) 1 2 0 0 0 1 3 0 0 2 1 6...
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