1.
PENERAPAN MATRIKS DALAM
ANALISIS SEKTOR
PEREKONOMIAN
Oleh:
Rohani Septiana Manurung 119166018
Dea Christin Carolina 119160089

2.
Pendahuluan Teori Aplikasi
OUTLINE

3.
Pendahuluan
Relasi dan matriks adalah salah satu bagian dari ilmu matematika diskrit yang menarik
untuk dipelajari. Dalam hal ini relasi dan matriks dikembangkan dalam menganalisis
masukan dan keluaran dalam bidang ekonomi.
Masukan dan keluaran yang terbentuk yaitu dari sektor sektor produksi dan konsumen
terdistribusi secara acak yang membentuk hubungan / relasi yang bisa dianalisis.

4.
Teori
o Matriks Bujur Sangkar
o Matrik Diagonal
o Matrik Identitas
b. Jenis-jenis Matriks
Matriks merupakan kumpulan angka / bilangan
dalam bentuk segi empat yang terdiri dari baris
dan kolom. Notasi suatu matriks biasanya ditulis
sebagai berikut:
𝑀 =
𝑎11
𝑎21
𝑎12
𝑎22
… 𝑎1𝑗
… 𝑎2𝑗
⋮ ⋮ ⋱ ⋮
𝑎𝑖1 𝑎𝑖2
… 𝑎𝑖𝑗
a. Definisi Matriks
o Matriks Transpos
o Invers Matriks
o Matriks Transaksi
o Matriks teknologi

5.
Matriks Trasaksi
Langkah awal dalam analisis masukan-
keluaran adalah menyusun suatu tabel
yang berisi keterang-keterangan tentang
bagaimana keluaran suatu sektor
terdistribusi ke sektor-sektor lain sebagai
masukan dan ke pemakai akhir sebagai
barang konsumsi.
Hubungan terakhir input dan output
disajikan dalam bentuk Sebuah tabel
yang disebut matriks transaksi, seperti
table disamping.

6.
Matriks Teknologi
Koefisien teknologi adalah suatu rasio yang menjelaskan
jumlah nilai keluaran sektor i yang diperlukan sebagai
masukan unit di sektor j terhadap jumlah total masukan
pada sektor j.
Matriks Teknologi terbentuk dari sejumlah koefisien
teknologi 𝑎𝑖𝑗 yang terbentuk dari elemen matriks transaksi

7.
Sedangkan nilai yang tidak konstan dibentuk dalam
matriks kolom, yaitu permintaan akhir (U) dan keluaran
total (V).
Dari persamaan dan matriks di atas dapat dibuktikan
persamaan yang menunjukkan hubungan kedua peubah
tersebut (U dan V) adalah

8.
dan dibentuk perkalian matriks menjadi :
berdasarkan fungsi balikan matriks juga berlaku:
𝑉 = 𝐼 − 𝑀 −1
𝑈
keterangan:
V : Matriks “keluaran total”
U : Matriks “permintaan akhir”
A : Matriks “koefisien teknologi”
I : Matriks Identitas

9.
Aplikasi
Masukan
keluaran
P I J PA T
P 20 35 115 30 200
I 100 75 20 80 275
J 30 82 15 190 317
NT 25 90 200 50 365
T 175 282 350 350 1.157
Keterangan
P : Sektor Pertanian
I : Sektor Industri
J : Sektor Jasa
NT : Nilai Tambah
PA : Penilaian Akhir
T : Keluaran Total

10.
Pemerintah menargetkan masing – masing :
1. Pertanian : ditingkatkan dari 30 menjadi 250
2. Industri : ditingkatkan dari 80 menjadi 125
3. Jasa : diturunkan dari 190 menjadi 100

11.
𝑀 =
20
175
35
282
115
350
100
175
75
282
20
350
30
175
15
282
15
350
=
0,1 0,1 0,3
0,5 0,2 0,05
0,1 0.05 0,04
Target permintaan akhir (U)
𝑈 =
250
125
100
Matriks M mendefinisikan matriks teknologi dengan elemen
pembentuknya adalah koefisien teknologi pada tabel di atas.

12.
Berdasarkan Persamaan berikut:
𝑉 = 𝐼 − 𝑀 −1
𝑈
misal 𝐵 = (𝐼 − 𝑀)
(𝐼 − 𝑀) =
1 0 0
0 1 0
0 0 1
−
0,1 0,1 0,3
0,5 0,2 0,05
0,1 0.05 0,04
= −
0,9 −0,1 −0,3
0,5 0,8 −0,05
−0,1 −0.05 0,96
Maka:

13.
Dengan metode kofaktor
𝐼 − 𝑀 −1
=
1
𝑑𝑒𝑡 𝐼 − 𝑀
𝐶𝑖𝑗
𝑇
(𝐼 − 𝑀)−1
=
1,2070 0,1822 0,4023
0,7964 1,3695 0,3202
0,1724 0,0903 1,1002
Maka
𝑉 = 𝐼 − 𝑀 −1
𝑈
𝑉 =
1,2070 0,1822 0,4023
0,7964 1,3695 0,3202
0,1724 0,0903 1,1002
250
125
100
=
364,755
402,307
164,407

14.
Setelah melakukan perhitungan tersebut maka masing-masing sektor harus
memasang keluaran total sebesar:
1. Pertanian : ditingkatkan dari 175 menjadi 364,755.
2. Industri : ditingkatkan dari 282 menjadi 402,307.
3. Jasa : diturunkan dari 350 menjadi 164,407.

15.
Referensi
Dumairy. (1999). Matematika Terapan untuk Bisnis dan Ekonomi. BPFE, 317.
Rahayu, Y. (2012). IMPLEMENTASI MATRIKS PADA MATEMATIKA BISNIS DAN
EKONOMI. Techno.COM, 74-81.
yapfrine, S. J. (2015). Penerapan Matriks dalam Analisis Sektor Perekonomian
Indonesia. Makalah IF2123 Aljabar Geometri, 1-2.

16.
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17.
Introduction
Mercury’s name has nothing to do
with the liquid metal, since this
planet was named after the
Roman messenger god

18.
Introduction
Mercury’s name has nothing to do
with the liquid metal, since this
planet was named after the
Roman messenger god

19.
The Teacher
Mercury is the closest
planet to the Sun and the
smallest one in the Solar
System—it’s only a bit
larger than the Moon

20.
Class Schedule
10:00 14:00 18:00
MONDAY Theory Exercise Review
TUESDAY Theory Exercise Review
WEDNESDAY - - -
THURSDAY Theory Exercise Test
SATURDAY Review Test Results

21.
Theory
01
You can enter a subtitle here if you
need it

22.
Concepts
Venus has a beautiful
name and is the second
planet from the Sun
Venus
Mercury is the closest
planet to the Sun and the
smallest one
Mercury

23.
It’s the closest
planet and the
smallest in the
Solar System
Mercury
It has a beautiful
name and is the
second planet
from the Sun
Venus
Despite being
red, Mars is a
cold place full of
iron oxide dust
Mars
What Is This Topic About?

24.
List of Operations
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25.
It has a beautiful name and is
the second from the Sun
Venus
It’s a gas giant and the
biggest planet of them all
Jupiter
Mercury is the closest planet
to the Sun and the smallest
Mercury
Features of the Topic
Despite being red, Mars is
actually a cold place
Mars

26.
Algebraic Numbers
Venus is terribly
hot
30%
Mars is a cold
place
50%
Saturn has
several rings
70%

27.
Graphs and Equations
To modify this graph, click on it, follow the link,
change the data and paste the new graph here Mars Venus
It’s the smallest
planet in the Solar
System
45%

28.
A Picture Is Worth a
Thousand Words

29.
Exercise Instructions
Mercury is the
closest planet to
the Sun
Mercury
Venus has a
beautiful name,
but it’s terribly hot
Venus
Despite being red,
Mars is actually a
cold place
Mars
It’s the biggest
planet in the Solar
System
Jupiter
Saturn is the
ringed one and a
gas giant
Saturn

30.
Practical Exercise
1
10
Maria
1
12
Kayla
1
X
Together
Mercury’s name has nothing to do with the liquid metal, since
this planet was named after the Roman messenger god

31.
Mercury is the
closest planet to
the Sun
Mercury
Example
Mars is a cold
place. It’s full of
iron oxide dust
Mars

32.
Mars
Curiosities Around the World
Despite being red,
Mars is a cold place
Mercury
Mercury is the
smallest planet

33.
Recommendations
Mercury is the
closest planet to
the Sun
Mercury
It’s the biggest
planet in the Solar
System
Jupiter
Saturn is the
ringed one and a
gas giant
Saturn
Despite being red,
Mars is actually a
cold place
Mars
Neptune is the
farthest planet
from the Sun
Neptune
Venus has a
beautiful name, but
it’s terribly hot
Venus

34.
3x²+5x
Big numbers catch your
audience’s attention

35.
Upcoming Workshops
Mercury is the
closest planet to
the Sun
09/20
Despite being red,
Mars is actually a
cold place
11/20
Saturn is the
ringed one and a
gas giant
02/21

36.
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