MAA111 ALGEBRA

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TEAM MEMBERS

Provide exclusive lanes for public transport

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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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NUR FATIHAH BINTI REZUAN

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

M UIZ FAHMI BIN JAMRAN

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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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Speaking : Nurhazwani

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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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

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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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D iscussion

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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

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Objectives

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01

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Study Objectives

Mercury

Mercury is the closest planet to the Sun and the smallest one in the Solar System

Neptune

Neptune is the farthest planet from the Sun and the fourth-largest by diameter in the Solar System

Jupiter

Despite being red, Mars is a cold place. It’s full of iron oxide dust, giving the planet its reddish cast

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Application of Linear Algebra in Traffic Flow

Images reveal large amounts of data, so remember: use an image instead of long texts

IDEA

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Literature Review

Theory 1

Mercury is the closest planet to the Sun and the smallest one in the Solar System

Theory 2

Venus has a beautiful name and is the second planet from the Sun

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Schedule

March

January

February

April

Mercury is the smallest planet

Venus has a beautiful name

Despite being red, Mars is cold

Saturn is the ringed planet

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A Picture Is Worth a Thousand Words

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Methodology

Research

Venus is the second planet from the Sun

Data Study

Despite being red, Mars is actually a cold place

Analysis

Jupiter is the biggest planet in the Solar System

Comparison

Saturn is composed mostly of hydrogen and helium

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Table

Test 1 Test 2 Test 3 Test 4 Concept 1 Concept 2 Concept 3 Concept 4

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Results Analysis

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Mars

Jupiter

Saturn

Venus

51%

Concept 1

49%

Concept 2

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Results Analysis

78.89%

Large-sized numbers catch your audience’s attention

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Jupiter is a gas giant and the biggest planet in the Solar System

Here you can describe the sample chosen for the study Here you can describe the sample chosen for the study Here you can describe the sample chosen for the study

Sampling

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Here you can explain the conclusions Here you can explain the conclusions Here you can explain the conclusions

Here you can explain the conclusions Here you can explain the conclusions Here you can explain the conclusions

Conclusions

Conclusion 1

Conclusion 2

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Reviewing Concepts

Mercury

Mercury is the closest planet to the Sun

Venus

Venus is the second planet from the Sun

Mars

Despite being red, Mars is actually a cold place

Jupiter

It’s the biggest planet in the Solar System

Saturn

Saturn is composed mostly of hydrogen and helium

Neptune

Neptune is the farthest planet from the Sun

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References

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Thanks!

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