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Applied Finite Mathematics HW Solutions 66

Applied Finite Mathematics HW Solutions 66 - '1 s4...

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Unformatted text preview: «'1: _ s4 _ EXERCiSES 3.6 32. 'DGHH (a) Using the fact that the number of cars entering each intersection must be equal to the number leaving it, we find the following four equations that must be satisfied by f1 .' f2, f3, ' and f4: 50+.f2 = f3: ‘ f3 = 504-131. 70+.f4 = fl: 'f1=50+f2- (b) When we write the system in the form f1 _ f2 2 60: ft "" f4 = 70: f2 "f3 = "-50: f3 "'f4 = 60. the augmented matrix is —1 0 0 60 1 -1 0 0 60 R1~+R2+R1 0 0 --1 70 R2——I-R1+R2 ___) 0 1 0 -—1 10 -1 -—1 D "50 D 1 -—1 0 “50 _R3——I~R2+Ra 0 1 #1 60 0 0 1 -1 60 100—170 100-170 _) 010—410 _ _"+ 010—110 {Jo-"114301236423 001460 001 ——1_ 60 001w16034HmR3+R4 1 0 0 -1 70 ___) D 1 D --1 10 0 D 1 --1 60 0 0 0 0 0 When we convert this augmented matrix back to an equivalent system of equations, we get fluf4=701 f2_f4:101 fanf4=60. Thus, there is an infinity of solutions, f1 =70+f4. f2 =10+f4. f3 =60+f4- Parameter f4 must be a nonnegative integer. (c) Portion f2 carries the least, and f1 carries the most. ' EXERCISES 3.6 6. 7. This is not a square matrix. It cannot have an inverse. This is not a square matrix. It cannot have an inverse. _‘__-_| L“ a“- -...-...a.......1 :_ ..........t....M...:n.. was...” I-...t...n.-n..:..s..:+.mruan:inh. nMIucm UntrHIm-nmrllud:m :n nun-I nr :n a." :& dHMIumfilikflM _--’_““x ...
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