Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: e 8.2.1. Use an augmented matrix to transform into triangular form. Solve the system. 3x − y + z = x + 2y − z = 2x + 3y − 4z = the following system of linear equations 8 4 10 Solution. We ﬁrst encode the system into an augmented matrix. 3 −1 18 3x − y + z = 8 Encode into the matrix x + 2y − z = 4 2 −1 4 −− − − − − −→ 1 −−−−−−− 2x + 3y − 4z = 10 2 3 −4 10 Thinking back to Gaussian Elimination at an equations level, our ﬁrst order of business is to get x in E 1 with a coeﬃcient of 1. At the matrix level, this means getting a leading 1 in R1. This is in accordance with the ﬁrst criteria in Deﬁnition 8.4. To that end, we interchange R1 and R2. 3 −1 18 1 2 −1 4 Switch R1 and R2 1 2 −1 4 − − − − − − 1 8 − − − − − → 3 −1 2 3 −4 10 2 3 −4 10 8.2 Systems of Linear Equations: Augmented Matrices 469 Our next step is to eliminate the x’s from E 2 and E 3. From a matrix standpoint, this means we need 0’s below the leading 1 in R1. This guarantees the leading 1 in R2 will be to the right of the leading 1 in R1 in accordance with the second requirement of Deﬁnition 8.4. 4 1 2 −1 4 1 2 −1 Replace R2 with −3R1 + R2 3 −1 1 8 −−...
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## This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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