GROUP 5 PROJECT 1

Money in UUM?

CONTENT

Background Of UUM 01
Background of Consumer Club 02
Letter from Student 03
Financial Tips 04

Budget Suggestions 07

Methods to Help Student 08
Cramer's Rule 11
Reduced Row-Echelon Form 12
System of Linear Equation 09

Type of Solution 10
28
Comparison Between Suggested

Budget and Total Budget

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BACKGROUND UUM was established on 16 February 1984 under the Universiti Utara
Malaysia 1984. Until this day, the main goal of founding this unique
sixth public university has been to educate and generate a critical
mass of business and management experts for the domestic and global
markets.

The Universiti Utara Malaysia (UUM) Badlishah Mosque, the Mu’adzam
campus is located in Sintok. The Shah Hall, the Tan Sri Othman Hall,
beautiful scenery, lush tropical the Sports Complex, the University
forests, and undulating hills surround Mall, the Student Residential Halls,
the 1,061- hectare campus, which the Executive Development Centre,
was originally a tin mining area. The and the University Inn. UUM offers
main buildings in the campus include undergraduate and postgraduate
the academic buildings, the Sultanah programmes that are conducted by
Bahiyah Library, the Administration three Academic Colleges, namely
buildings, the Chancellery, the Sultan UUM College of Arts and Sciences
(UUM CAS), UUM College of
Business (UUM COB), and UUM
College of Law, Government and
International Studies (UUM COLGIS).

SQQM 2023 | A212 | June Edition | 2022 page 1

CONSUMER
CLUB UUM

BACKGROUND Universiti Utara Malaysia has so many clubs and associations that
offer great opportunities for students to gain knowledge and
experience. Clubs and associations are created for students to
explore new things, develop their skills in preparing for events, and
be a better person in the workplace in the future. The consumer club
uum is one of the clubs in uum.

Consumer Club UUM is an effort Our mission is to help students
aimed at increasing student understand the fundamental
community awareness of rights of a citizen, as well as to
consumer rights and duties. Our make them aware of and learn
mission is to raise consumer the fundamental duties of a
rights awareness across all good citizen; to instil knowledge
consumer sectors, particularly and skills about consumer rights
college students, and to reach in our college students, as well as
the unreached by providing knowledge about product
knowledge and training on standards, product quality, and
consumer rights to our students markets;
and empowering them to teach
village employees.

Since its foundation, the club has held a number of outreach
programmes, consumer awareness demonstrations, guest lectures,
training of trainers, competitions, and so on. Our consumer club also
received the District Collector, Consumer Department, Jitra District's
"Best Club" award at the district level.

SQQM 2023 | A212 | June Edition | 2022 page 2

Hi admin of Consumer Club UUM. Blok A,
My name is Amri. I am a first year INASIS Grantt.
Business Mathematics student in
Universiti Utara Malaysia (UUM).
This is the first time I live and went
far away from home. Hence, this is
also the first time I manage my own
money. First few weeks in UUM, I
spent my money lavishly. I just
realize now that I need to spend
wisely. Therefore, I want to count
the money that I have been spending
and know either I am overspending or
underspending. Can admin help me
count and tell me few financial tips
and how to budget my money
properly.

THIS Does not
MIGHT have enough

BE money
AMRI
IF HE Hungry Lack of
DO NOT motivation
SPEND HIS
MONEY
WISELY

SQQM 2023 | A212 | June Edition | 2022 page 3

System of Linear Equation

IS THE STUDENT'S

BUDGET RELEVANT?

Important of budgeting

Budgeting is an essential component of living
a financially healthy life. It enables people to
build a spending plan for their money. It can
also ensure that they always have enough
emergency money. Budgeting is very
important to university students who should
spend their money between study and daily
living expenditures.
Furthermore, budgets also teach students
how to be aware when they are overspending
or underspending. It can also manage their
finances in the future and teach them to be
smart when shopping and using money.

Tips in budgeting What are the uses of linear equations
in budgeting? Is it possible for students to
Calculate your net income use linear equations to help them make a
Your monthly income is an essential element budget?
of your budget since it creates the maximum
on how much you can spend. In general, we understand that linear
List montly expense algebra is a system with its own unknown,
Organize your expenses into fixed and which we must solve using the linear
variable categories algebra method. We can calculate the price
of each item spent using the linear concept
Fixed expenses the costs you must incur of algebra and can compare under-budget
for things like your study fees, meals, or over-budget in an indirect way. This is a
transportation, and other. concept that may be used to create an
Variable expenses things like dinner costs, effective budget and help students in
additional groceries, and other expenses effectively managing their finances.
that are not monthly payments.
Determine average monthly cost for each
expense
Make adjustments
The final step is to estimate all monthly
expenses and compare them to the
prepared budget. Next, identify which costs
are excessive and inadequate. If expenses
exceed your budget, you must reorganise
your new budget; if they don't, you must put
the remaining funds into the following
month's budget.

SQQM 2023 | A212 | June Edition | 2022 page 4

LIST OF THINGS THAT AMRI
WANTS TO BUY AT STORE

BREAD

BISCUIT

SNACKS

MAGGIE

SQQM 2023 | A212 | June Edition | 2022 page 5

3 IN 1 DRINK

FACE MASK

SQQM 2023 | A212 | June Edition | 2022 MINERAL
WATER

page 6

BUDGET SUGGESTION

The admin of consumer club UUM helped Amri by stating the
budget that Amri should spend throughout this 7 weeks

RM 60 RM 60 RM 60

RM 90 RM 50 RM 150

RM 30 TOTAL MONEY THAT AMRI SHOULD SPEND
IN 7 WEEKS IS RM500.

BY THE END OF WEEK 7, AMRI SHOULD

KNOW WHETHER HIS SPENDING EXCEED


THE BUDGET LIMIT OR NOT.

SQQM 2023 | A212 | June Edition | 2022 page 7

There are two methods that can be use to
solve Amri's problem:

Using CRAMER'S Using Reduced
RULES Row Echelon
Form (RREF)

Let x1: Bread
x2: Biscuits
x3: Instant Noodles
x4: Mineral Water
x5: 3 in 1 Drinks
x6: Snacks
x7: Face masks

System of linear equations:

x1 + x2 + 3x3 + x4 + x6 + x7 = 83
2x1 + x3 + x5 + 2x6 = 75
x1 + 2x2 + 2x4 + x6 + x7 = 82
x1 + x3 + 2x5 + 3x6 = 102
x1 + 3x2 + x4 + x6 + x7 = 76
x1 + x2 + x5 + x6 = 53
x1 + x3 + x4 + 2x6 + x7 = 70

SQQM 2023 | A212 | June Edition | 2022 page 8

SYSTEM OF
LINEAR
EQUATION
LINEAR ALGEBRA MAGAZINE

AA lliinneeaarr eeqquuaattiioonn iinn tthhee vvaarriiaabblleess

AA lliinneeaarr eeqquuaattiioonn iiss nnoott aallwwaayyss iinn


xx11,,......,,xx22 iiss aann eeqquuaattiioonn tthhaatt ccaann bbee

tthhee ffoorrmm yy == 11..66 −− 11..22xx,,
wwrriitttteenn iinn tthhee ffoorrmm IItt ccaann aallssoo bbee lliikkee yy == 00..22((88 −− 66xx))
oorr lliikkee yy ++ 11..22xx == 11..66
aa11xx11 ++ aa22xx22 ++ ...... ++ aannxxnn == bb oorr lliikkee yy ++ 11..22xx −− 11..66 == 00 aanndd mmoorree..

wwhheerree bb aanndd tthhee ccooeeffffiicciieennttss

NNoottee:: TThhoossee aarree aallll tthhee ssaammee lliinneeaarr


aa11,,......,,aann aarree rreeaall oorr ccoommpplleexx

eeqquuaattiioonn!!
nnuummbbeerrss,, uussuuaallllyy kknnoowwnn
iinn aaddvvaannccee..

AA ssyysstteemm ooff lliinneeaarr eeqquuaattiioonnss ((oorr aa


lliinneeaarr ssyysstteemm)) iiss aa ccoolllleeccttiioonn ooff oonnee


oorr mmoorree lliinneeaarr eeqquuaattiioonnss iinnvvoollvviinngg


tthhee ssaammee vvaarriiaabblleess ssuucchh aass xx11,, xx22,,


xx33,, ......,, xxnn..

EExxaammppllee iiss::
22xx11 -- xx22 ++ xx33 == 2200
xx11 -- 22xx33 == --1100

SQQM 2023 | A212 | June Edition | 2022 page 9

TYPE OF SOLUTION

NO SOLUTION

INFINITELY MANY
SOLUTION

ONE SOLUTION

SQQM 2023 | A212 | June Edition | 2022 page 10

WHAT IS
CRAMER'S RULE ?

Cramers rule is a technique to solve systems of linear equations where there
are the same amount of unknowns as equations in the system. The
technique consists on a set of equations involving determinants and ratios in
order to obtain the unique set of solutions for a linear system.

1 Determine whether 2 Fails for the 3 Provides the
the given system has system of
“no solution” or results only
“infinite number of equations in
solutions” when
which
Determinant ≠ 0
Determinant = 0

The Formula is given by : For the example :

This example solve by using Excell 1
0
D= 1 1 3 1 0 1 1

20 1 0 1 2 0

1 2020 1 1

1 0 1 023 0

1 301 0 1 1

1 1 00 1 1

1 0 1 1 02

For using the formula we need to D = -9
expresses the solution in terms of the The determinant can be calculated using
determinants of the coefficient matrix (i.e., excell by
for a square matrix) and of matrices set fuction ["=MDETERM(array)"].
obtained from it by replacing one column
by the column vector of right-hand-sides
of the equations.

SQQM 2023 | A212 | June Edition | 2022 page 11

What is Reduced

Row Echelon Form?

A matrix is in reduced row echelon form (RREF) if it satisfies this
four conditions :

Nonzero rows appear above the zero rows.
Each leading entry of a row is in a column to the right of the
leading entry of the row above it.
Each leading entry must be a 1.
All entries in column below and above a leading 1 are zeroes.

Example of RREF:

By executing a sequence of operations on the rows of the matrix, any
matrix may be turned into its RREF. The typical strategy is start by
converting the items in the lower left to zeros. The last step is to convert all
of the entries above the leading ones to zeros. The operation is called ERO.

Divide a row by a Operation of Interchange
nonzero number Elementary Row two rows
Operation (ERO):

Subtract a
multiple of a row
from another row

SQQM 2023 | A212 | June Edition | 2022 page 12

Using CRAMER'S
RULES

SOLUTION :

The solution given by :

x1 = D1/D x4 = Dx4/D x7 = Dx7/D
= -72/-9 = -144/-9 = -63/-9
=8 = 16 =7

x2 = Dx2/D x5 = Dx5/D
= -90/-9 = -180/-9
= 10 = 20

x3 = Dx3/D x6 = Dx6/D
= -81/-9 = -135/-9
=9 = 15

SQQM 2023 | A212 | June Edition | 2022 page 13

Using Reduced Row
Echelon Form (RREF)

Transform into Reduced Row Echelon Form
(RREF):

Hence, the solution for Amri's item is: page 14
x1 = 8
x2 = 10
x3 = 9
x4 = 16
x5 = 20
x6 = 15
x7 = 7

SQQM 2023 | A212 | June Edition | 2022

total price for each items that Amri
bought for 7 weeks

x1= Bread = RM8 The total purchase of bread is
RM56
x1 +2x1+ x1 +x1 + x1 + x1 + x1
= 8 + 2(8) + 8 + 8 + 8 + 8 + 8
= RM56

x2= Biscuits = RM10 The total purchase of biscuits is
RM70
x2 + 2x2 + 3x2 + x2
= 10 + 2(10) + 3(10) +10
= RM70

x3= Instant Noodles = RM9 The total purchase of instant
noodles is RM54
3x3 + x3 + x3 + x3
= 3(9) + 9 + 9 + 9
= RM54

x4=Mineral Water = RM16 The total purchase of mineral
water is RM80
x4 + 2x4 + x4 + x4
= 16 + 2(16) + 16 + 16
= RM80

SQQM 2023 | A212 | June Edition | 2022 page 15

total price for each items that Amri
bought for 7 weeks

x5=3 in 1 Drink = RM20 The total purchase of 3 in 1
drinks is RM80
x5 + 2x5 + x5
= 20 + 2(20) + 20
= RM80

x6= Snacks = RM15 The total purchase of snacks is
RM165
x6 + 2x6 + x6 + 3x6 + x6 + x6 + 2x6
= 15 + 2(15) + 15 + 3(15) + 15 + 15 +
2(15)
= RM165

x7= Face mask = RM7 The total purchase of facemask
is RM28
x7 + x7 + x7 + x7
=7+7+7+7
= RM28

SQQM 2023 | A212 | June Edition | 2022 page 16

COMPARISON BETWEEN

SUGGESTED BUDGET WITH TOTAL


BUDGET THAT AMRI SPENT

Budget BREAD Amri
Limit Spent
BISCUITS
RM 60 RM 56
INSTANT
RM 60 NOODLES RM 70

RM 60 RM 54

RM 90 MINERAL RM 80
WATER

RM 50 3 IN 1 DRINKS RM 80
RM 150 SNACKS RM 165
RM 30 RM 28
FACEMASK

The total money that Amri spent in 7 weeks is RM 533.
Since the consumer club has fixed the amount that he
should spend for 7 weeks is RM500, then Amri has
exceeded the budget given. From the above, we can see
which type of items that he overspent during this 7
weeks.

SQQM 2023 | A212 | June Edition | 2022 page 17

CONCLUSION

In conclusion, the two methods used to calculate Amri's
budget are very useful in order to help Amri solve his
problems. By using Creamer's Rules and using Reduced Row
Echelon Form (RREF), we can justify the price of each item
that Amri buys at the store. The two methods help Amri
calculate the total cost of the items, which are bread, biscuits,
instant noodles, face masks, snacks, and mineral water. At the
end of the calculation, we know that Amri has exceeded the
limit of budget spending. This will give Amri an idea of their
total spending during the total 7 weeks of university and will
allow him to make a plan and manage his money to survive
during university life.

Besides, the two methods, which are Creamer's Rules
and Reduced Row Echelon Form (RREF), can also be useful in
our daily lives. This method can also be used in complex
numbers, which are necessary for solving certain problems
with real number answers and not just a convenient device in
such problems that could be replaced by real numbers, as in
solving certain cubic equations.

SQQM 2023 | A212 | June Edition | 2022 page 18

REFERENCES from

MAT 263. (n.d.). Prezi.Com. Retrieved June 19, 2022,
https://prezi.com/p/s2-f5ji2nj56/mat-263/

Mint. (2020, August 4). 18 budgeting tips to make money management easy.
MintLife Blog. https://mint.intuit.com/blog/budgeting/tips/

Nishitha. (2021, March 1). Applications of linear equations in real life.
WittySparks. https://wittysparks.com/linear-equations-in-real-life-examples/

Row Echelon Form & Reduced Row Echelon Form. (2021, January 29). Statistics
How To. https://www.statisticshowto.com/matrices-and-matrix-algebra/reduced-
row-echelon-form-2/

Crow, S. [crowsmathclass]. (2017, April 8). Cramer’s Rule using Excel to solve
system of equations. Youtube. https://www.youtube.com/watch?v=yTYObct_88E

Solving linear systems using Cramer’s Rule. (n.d.). Studypug.Com. Retrieved
June 25, 2022, from https://www.studypug.com/algebra-help/solving-linear-
systems-using-cramers-rule

SQQM 2023 | A212 | June Edition | 2022

REFLECTION

NADHIRAH AFIFAH BINTI NORZEKRY 280510

I would like to express my gratitude to Prof. Dr. Haslinda for
her assistance with this project. In class, we discuss many
things to help us comprehend about the System of Linear
Equation. My favourite thing about this project is I get to
widen my knowledge about the application of System Of
Linear Equation in daily life. I would never figure out that we
can use what we learn in daily life. All this while, I only
thought that we will be learning this for exam purposes
only. Even though it was difficult for me at first, I am still
enjoying the learning process. Last, I am very glad to
accomplish this project.

FITRAH NUR AYUNIE BINTI AMIRUDDIN 280910

First of all, I would like to say that this was an
interesting learning experience I have ever had. I
learned lot of things relating system of linear
equations while completing this task. So I would like to
express my deepest gratitude especially to Prof. Dr.
Haslinda for giving a guidance and advice throughout
this project and thank you to my groupmates for
sharing the ideas and knowledges for this project. I
really enjoyed it.

SQQM 2023 | A212 | June Edition | 2022

REFLECTION

muhammad zuhair afham bin mohd nasir 280782

This project is an interesting one as my groupmates
and I have to create a real situation related to the
system linear equation. The best part is that we have
to create a story in which one of the UUM students,
Amri, wants to budget his expenses during university
life. After all of these things, we need to suggest that
his budget not exceed the budget limit that they set.
After all, I want to take this opportunity to thank my
groupmates-Nadhirah, Ayunie, and Sarah-and lecturer
Prof. Dr. Haslinda for giving us advice on how we could
improve our project when we were presenting our
project draft. I've definitely learnt more about linear
algebra in a fun way!

sarah afifah binti azeman 280611

I want to start by thanking Prof. Haslinda and my pals for
their assistance in getting this project group finished. By
putting this project group in reality, I was able to learn
more about the uniqueness of this linear algebra topic. It
can also help me in developing my critical thinking and
creativity. By using the idea of linear algebra to solve a
problem, I can learn many things in this life when I take
this project in reality. in addition, this project is also one
of the learning methods that is very effective for me in
further understanding the subject.

SQQM 2023 | A212 | June Edition | 2022

APPENDIX

Solution of Cramer's rule using Excel :

SQQM 2023 | A212 | June Edition | 2022

The solution of Cramer's rule using Excell :

SQQM 2023 | A212 | June Edition | 2022

The solution of RREF using Excell :

SQQM 2023 | A212 | June Edition | 2022

The solution of RREF using Excell :

SQQM 2023 | A212 | June Edition | 2022

The solution of RREF using Excell :

SQQM 2023 | A212 | June Edition | 2022

The solution of RREF using Excell :

SQQM 2023 | A212 | June Edition | 2022