Stitz-Zeager_College_Algebra_e-book

3x 5 3 31 5 5 3 31 5 5 associative property

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Unformatted text preview: 2) 2x1 + x2 − x3 = 4 (E 3) x2 − 3x3 − 2x4 = 0 3 2 0 1 1 (E 1) x1 + 3 x2 + 3 x4 = 2 (E 2) 2x1 + x2 − x3 = 4 −−−−−−− −−−−−−→ (E 3) x2 − 3x3 − 2x4 = 0 Replace E 1 with 1 E1 3 1 0 16 1 Replace R1 with 1 R1 1 −1 0 4 − − − − − −3− − − − − − −→ 2 1 −3 −2 0 0 1 3 1 0 32 1 −1 0 4 1 −3 −2 0 Finally, we have an example of replacing a row with itself plus a multiple of another row using the second step from part 2 in Example 8.1.2. 1 We shall study the coefficient and constant matrices separately in Section 8.3. 468 Systems of Equations and Matrices (E 1) x + 3 y − 1 z = 2 2 (E 2) 10x − z = (E 3) 4x − 9y + 2z = 1 3 1 2 −2 10 0 −1 4 −9 2 1 2 2 5 1 2 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 1 1 3 1 2 −2 2 Replace R2 with −10R1 + R2 2 − − − − − − − − − → 0...
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