Stitz-Zeager_College_Algebra_e-book

The remaining properties are left to the reader the

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Unformatted text preview: y + z = Replace E 2 with −2E 1 + E 2 (E 2) −2y + z = 6 −− − − − − − − −→ −−−−−−−−− Replace E 3 with −3E 1 + E 3 (E 3) 2y − 2z = −12 If letters are used instead of subscripted variables, Definition 8.3 can be suitably modified using alphabetical order of the variables instead of numerical order on the subscripts of the variables. 458 Systems of Equations and Matrices Now we enforce the conditions stated in Definition 8.3 for the variable y . To that end we need to get the coefficient of y in E 2 equal to 1. We apply the second move listed in Theorem 8.1 and replace E 2 with itself times − 1 . 2 5 (E 1) x − y + z = (E 2) −2y + z = 6 (E 3) 2y − 2z = −12 5 (E 1) x − y + z = (E 2) y − 1 z = −3 −−−−−−−→ −−−−−−− 2 (E 3) 2y − 2z = −12 Replace E 2 with − 1 E 2 2 To eliminate the y in E 3, we add −2E 2 to it. 5 (E 1) x − y + z = 1 (E 2) y − 2 z = −3 (E 3) 2y − 2z = −12 5 (E 1) x − y + z = Replace E 3 with −2E 2 + E 3 1 (E 2) y − 2 z = −3 −− − − − − − − −→ −−−−−−−...
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