Unformatted text preview: move on to
the next variable, in this case y , and repeat. Since the variables in all of the equations have
a consistent ordering from left to right, our ﬁrst move is to get an x in E 1’s spot with a
coeﬃcient of 1. While there are many ways to do this, the easiest is to apply the ﬁrst move
listed in Theorem 8.1 and interchange E 1 and E 3. 3x − y + z = 3 (E 1)
(E 2) 2x − 4y + 3z = 16 (E 3)
x−y+z = 5 x−y+z = 5 (E 1)
Switch E 1 and E 3
(E 2) 2x − 4y + 3z = 16
−− − − − −
− − − − −→ (E 3)
3x − y + z = 3 To satisfy Deﬁnition 8.3, we need to eliminate the x’s from E 2 and E 3. We accomplish this
by replacing each of them with a sum of themselves and a multiple of E 1. To eliminate the
x from E 2, we need to multiply E 1 by −2 then add; to eliminate the x from E 3, we need to
multiply E 1 by −3 then add. Applying the third move listed in Theorem 8.1 twice, we get x−y+z = 5 (E 1)
(E 2) 2x − 4y + 3z = 16 (E 3)
3x − y + z = 3
12 5 (E 1) x −...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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