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1379705214_785__232a3 (1)

# 2 52 sum the three equalities multiplied by

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Unformatted text preview: nts, to cancel x, y, z and obtain a linear equation in terms of a, b, c. 2.2: (self-study) D1 there is exactly one solution 9 VI.1 Sophie 10 2.2: D5 (a) 3, (b) 5, (c) 3 12 A.3/ C Introduction to Prob. Mariolys 2.2: D6 (a) 3, (b) 3, (c) 3 2.2: D7 18 F, (b) F, (c) F, (d) T (a) IX.1 Limit Laws and Comb Marni 11 2.2: D8 (a) T, (b) F, (c) F, (d) F IX.2 Discrete Limit Laws Sophie 2.2: D920 there are eighteen Random Structures solutions embracing all possible combinations with α ∈ {0, π, 2π }, β ∈ {π/2, 3π/2}, and γ ∈ {0, π, 2π }. No and Limit Laws contradiction: Theorem 2.2.1 only speaks of linear equations. FS: Part C Combinatorial 23 IX.3 2.3: 2 (a) x1 + x3 = 200, x1 − x2 = −25, x2 + x4 i− x6 = of discrete x4Mariolys −150, x5 + x6 = 200, (b) x1 = −s + t + 150, x2 = −s + t + 175, − x5 = (rotating nstances 175, x3 − 12 x3 = s − t + 50, x4 = s, x5presentations) , x6 = t for −∞ < s, t < ∞, (c) x1 = 100, x2 = 125, x3 = 100, x4 = 50, x5 = 200, x6 = 0. The = −t + 200 Continuous Limit Laws Marni positive25 ﬂows xIX.4x2 , x3 , x4 , x5 move in the direction of the arrows on the diagram. x6 = 0 represents no ﬂow. 1, 2.3: 4 (a) x1 + x3 = 800, x1 − x2 + x4 = 200, x2 − x5 = 500, and− x7 = −50, x4 + x6 − x7 = 600, x3 + x6 = 750, (b) x1 = s + 50, x2 = t + 450, Quasi-Powers x5 Sophie x3 13 −s + 750,IX.5 = −s + t + 600, x5 = t − 50,Gaussian,limit = t for −∞ < s, t < ∞, (c) it is not possible = 30 x4 x6 = s x7 laws 2.3: 10 the balanced equation is C6 H12 O6 → 2CO2 + 2C2 H5 OH 14 Asst #3 Due 3.1: 30 Dec 10 cj (B ) = ck (C ), then Presentations Acj (B ) = Ack (C ) = ck (AC ), (b) If rj (B ) = rk (C ), then rj (BA) = rj (B )A = rk (C )A = (a) If cj (AB ) = 01 rk (CA) 3.1: D2 One possible choice is A = 00 3.1: D4 Only one 3.1: D7 Yes 3.1: D8 Yes 3.1: D9 (a) F, (b) T, (c) T, (d) F, (e) T, (f) F Additional questions: A1. Full rank if and only if a ∈ {b, −b} A2. (a) {0, ∞}, (b) {0, 1, ∞} Dr. Marni MISHNA, Department of Mathematics, SIMON FRASER UNIVERSITY Version of: 11-Dec-09 C EDRIC C HAUVE , FALL 2013 4...
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