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Unformatted text preview: CHAPTER 1. INTRODUCTION TO VECTORS 53 SOLUTION. As usual, we eliminate $1 from equation (2). On subtracting 2 X equation (1) from equation (2)1 we obtain the new equation (2) as 0:131 + 0:122 + 0:133 = —6, (2!) which clearly has no solution. The geometric interpretation is that the planes represented by equations (1) and (2) are parallel and do not intersect. 0 Example 4. Find the solutions of the system 2:31 — 3.362 + $3 = 20 (1) 4:191 — 63:2 + 2583 = 40. (2) SOLUTION. Eliminating $1 from equation (2) gives the new equation (2) as 0331 + 03:2 + 0133 = 0. (2") The given system is thus equivalent to :r — €332 + %333 =10 (1*) 0.11:1 + 0:132 -|- 0.563 = 0 (2*) which has as standard parametric solutions: /:1:1\ /10\ /%\ / —% \ ...
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