1 2 2 1 3 3 1 2 r1 r2 1 2 1 3 1 2 2 3 2 1 3

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Unformatted text preview: s to solve systems? Let’s start with a system of two equations and two unknowns. ax + by = p cx + dy = q We first write down the augmented matrix for this system, éa b êc d ë pù qú û and use elementary row operations to convert it into the following augmented matrix. é 1 0 hù ê0 1 k ú ë û © 2007 Paul Dawkins 327 http://tutorial.math.lamar.edu/terms.aspx College Algebra Once we have the augmented matrix in this form we are done. The solution to the system will be x = h and y = k . This method is called Gauss-Jordan Elimination. Example 1 Solve each of the following systems of equations. 3x - 2 y = 14 (a) [Solution] x + 3y = 1 (b) -2 x + y = -3 [Solution] x - 4 y = -2 (c) 3 x - 6 y = -9 [Solution] -2 x - 2 y = 12 Solution (a) 3x - 2 y = 14 x + 3y = 1 The first step here is to write down the augmented matrix for this system. é3 -2 14 ù ê 1 3 1ú ë û To convert it into the final form we will start in the upper left corner and the work in a counterclockwise direction until the first two columns appear as they should be. So, the first step is to make the red three in the augmented matrix above into a 1. We can use any of the row operations that we’d like to. We should always try...
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