Stitz-Zeager_College_Algebra_e-book

# We motivate the general denition with an example

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Unformatted text preview: = 2 (E 3) 4x − 9y + 2z = 5 (E 1) x + 3 y − 1 z = 2 2 Replace E 1 with (E 2) 10x − z = −−−−−−− −−−−−−→ (E 3) 4x − 9y + 2z = 1 E1 2 1 2 2 5 Now it’s time to take care of the x’s in E 2 and E 3. 3 (E 1) x + 2 y − 1 z = 2 (E 2) 10x − z = (E 3) 4x − 9y + 2z = 1 2 2 5 3 1 (E 1) x + 2 y − 1 z = 2 2 Replace E 2 with −10E 1 + E 2 (E 2) −15y + 4z = −3 −−−−−−−−−→ −−−−−−−−− Replace E 3 with −4E 1 + E 3 (E 3) −15y + 4z = 3 8.1 Systems of Linear Equations: Gaussian Elimination 459 Our next step is to get the coeﬃcient of y in E 2 equal to 1. To that end, we have 1 1 (E 1) x + 3 y − 2 z = 2 2 (E 2) −15y + 4z = −3 (E 3) −15y + 4z = 3 3 (E 1) x + 2 y − 1 z = 2 Replace E 2 with 4 (E 2) y − 15 z = −− − − − − − − − − − − − − −→ (E 3) −15y + 4z = 1 − 15 E 2 1 2 1 5 3 Finally, we rid E 3 of y . 1 (E 1) x + 3 y − 2 z = 2 4 (E 2) y − 15 z = (E 3) −15y + 4z = 1 2 1 5 3 5 (E 1) x − y + z = Replace E 3 with 15E 2 + E 3 1 (E 2) y − 2 z = −3 −− − − − − − − − − −...
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