MAA111 ALGEBRA

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TEAM MEMBERS

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NUR FATIHAH BINTI REZUAN

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SITI AISYAH BINTI ABDUL RAAFI’

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NUR FATIHAH BINTI REZUAN

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SITI AISYAH BINTI ABDUL RAAFI’

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M UIZ FAHMI BIN JAMRAN

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SITI AISYAH BINTI ABDUL RAAFI’

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NURHAZWANI BINTI ROZALI

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NUR FATIHAH BINTI REZUAN

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Objective Introduction Methodology Analysis Conclusion

Contents

v [DEA

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Speaking : Siti Aisyah

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Objective

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To show how linear algebra is applied in the analysis of traffic flow through a road network including how systems of linear equation with many solutions can arise in practice.

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Speaking : Nur Fatihah

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INTRODUCTION

Speaking : Nur Fatihah

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Introduction

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Traffic flow is the study of interactions between vehicles, drivers, pedestrian, cyclists, other travelers and infrastructure with the aim of understanding and developing an optimal road network with efficient movement of traffic and minimal traffic congestion problems.

Speaking : Nur Fatihah

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Introduction

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Assume that we have data of number of cars passing through different intersections in one hour. This data can be obtained by periodic observations or through some sensors. Traffic flow will differ at the time of day or night.

Speaking : Nur Fatihah

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METHODOLOGY

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Speaking : Nurhazwani

The following assumptions were made in order to ensure that there is always smooth traffic flow

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The street is assumed to be one way. Number of vehicles entering the intersection is equivalent to the number of vehicles leaving the intersection

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ANALYSIS IN TRAFFIC FLOW

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Speaking : Nurhazwani

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Figure shows a roundabout in Georgetown, Penang.

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Multiple interweaving highways with cars driving in different directions

The equation obtained from previous picture :

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Assuming that there is no vehicles entering the intersection and there is no vehicles leaving the intersection. Therefore, the equations involved are: X 1 + X 2 = X 3 X 3 = 50 + 150 X 4 + 80 = X 1 150 = X 4 + 120

Speaking : Nurhazwani

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Next, we separate values of x and b into right hand side and left hand side. X 1 + X 2 - X 3 = 0 X 3 = 200 X 1 - X 4 = 80 X4 = 30 After that, we convert the system of linear equation into augmented matrix.

Speaking : Nurhazwani

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Speaking : Muiz Fahmi

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R 3 :R 3 -R 1

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R 3 :R 3 -R 1

R 3 ↔R 2

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R 3 :R 3 -R 1

R 3 ↔R 2

R 2 :R 2 /(-1)

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R 3 :R 3 -R 1

R 3 ↔R 2

R 2 :R 2 /(-1)

R 2 :R 2 -R 4

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Speaking : Muiz Fahmi

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R 3 :R 3 -R 1

R 3 ↔R 2

R 2 :R 2 /(-1)

R 2 :R 2 -R 4

R 2 :R 2 +R 3

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Speaking : Muiz Fahmi

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R 3 :R 3 -R 1

R 3 ↔R 2

R 2 :R 2 /(-1)

R 2 :R 2 -R 4

R 2 :R 2 +R 3

R 1 :R 1 +R 3

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Speaking : Muiz Fahmi

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R 3 :R 3 -R 1

R 3 ↔R 2

R 2 :R 2 /(-1)

R 2 :R 2 -R 4

R 2 :R 2 +R 3

R 1 :R 1 +R 3

R 1 :R 1 +R 3

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Speaking : Muiz Fahmi

X 1 = 110 X 2 = 90 X 3 = 200 X 4 = 30

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DISCUSSION

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D iscussion

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Speaking : Siti Aisyah

X 1 = 110 X 2 = 90 X 3 = 200 X 4 = 30

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D iscussion

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Speaking : Siti Aisyah

X 3 = 200 v/h

X 1 = 110 v/h

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D iscussion

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Speaking : Siti Aisyah

There are several ways to reduce the traffic congestion in the identified area

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Speaking : Siti Aisyah

Use public transport or car pool

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D iscussion

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Speaking : Siti Aisyah

Provide exclusive lanes for public transport

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D iscussion

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From the calculation, we can determine the number of vehicles passing through the road. On that time, the slowest traffic is at X 3 with 200 v/h, followed by X 1 with 110 v/h. After we have identified the number of vehicles passing through the road, then we can take action in order to reduce the traffic congestion. There are several ways to reduce the traffic congestion in the identified area : Provide exclusive lanes for public transport Car pool or use public transport

Speaking : Siti Aisyah