Please show all work.Use linear algebra and network analysis to solve this question. 16. The downtown core of Gotham City consists ofone-way streets, and the traffic flow has beenmeasured at each intersection. For the city blockshown in Figure 2.19, the numbers represent theaverage numbers of vehicles per minute entering andleaving intersections A, B, C, and D during businesshours.(a) Set up and solve a system of linear equations to findthe possible flows f₁... f₁.(b) If traffic is regulated on CD so that f = 10 vehiclesper minute, what will the average flows on the otherstreets be?(c) What are the minimum and maximum possibleflows on each street?(d) How would the solution change if all of the direc-tions were reversed?10ADFigure 2.19B515

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Answered: 16. The downtown core of Gotham City…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please show all work.

Use linear algebra and network analysis to solve this question.

16. The downtown core of Gotham City consists of
one-way streets, and the traffic flow has been
measured at each intersection. For the city block
shown in Figure 2.19, the numbers represent the
average numbers of vehicles per minute entering and
leaving intersections A, B, C, and D during business
hours.
(a) Set up and solve a system of linear equations to find
the possible flows f₁... f₁.
(b) If traffic is regulated on CD so that f = 10 vehicles
per minute, what will the average flows on the other
streets be?
(c) What are the minimum and maximum possible
flows on each street?
(d) How would the solution change if all of the direc-
tions were reversed?
10
A
D
Figure 2.19
B
5
15

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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