UNIVERSITAS ISLAM INDONESIA FAKULTAS MIPA
Jl. Kaliurang Km. 14,5 Jogjakarta
FINAL EXAM
ACADEMIC YEAR 2020/2021
Course : Linear Algebra for Statistics Study Program/Class : Statistics / A
Day/Date : Thursday/14 January 2020
Time : 120 minutes
Lecturer : Muhammad Hasan Sidiq K, M.Sc.
Exam Description : Buku terbuka Online Media : Google Classroom
And Allah makes an example for the believers, the wife of Pharaoh, when she said, "My Lord, build for me a house with You in Paradise and save me from Pharaoh and his deeds, and save
me from a people who unjust,"
Q.S. At-Tahrim 11 INSTRUCTIONS:
1. All answers are handwritten on paper, scanned and uploaded in PDF format.
2. You can use software R and Microsoft Excel to help the calculation process.
3. The PDF file naming format is: NIM_NAMA_ALJABAR(UAS).
4. The file must be uploaded no later than 4 p.m. WIB.
5. Don't forget to write your name in your answer file.
6. Work honestly and independently.
PLO: Mastering the concepts of probability theory and statistics, mathematics, calculus, elementary linear algebra, statistical analysis methods, and elementary computer programming.
LO: Students are able to perform operations on vectors, apply vectors in the field of statistics, and calculate values and eigenvectors.
Indicator: Students are able to interpret vectors in dimensional space, calculate vector lengths and angles, and calculate eigenvalues.
Pray first and don't be in a hurry J.
1. (Points: 10) Given three vectors in three dimensions 𝒂 = (−𝟏, 𝟒, −𝟑) 𝒃 = (𝟓, −𝟏, 𝟏) 𝒄 = (𝟏, 𝟐, 𝟑). Draw those three vectors.
2. Given the number of patients Covid-19 data on January 7, 2021 in all provinces on the island of Java (https://bnpb-inacovid19.hub.arcgis.com/).
Table 1. The number of Covid-19 patients on Java.
Province Number of Positive Cases (thousands) (X1)
Number of Recovered (thousands) (X2)
Number of Death Cases (thousands) (X3)
DKI Jakarta 195,3 175,3 3,3
Jawa Barat 91,1 77,5 1,2
Jawa Tengah 87,6 60 3,9
Daerah Istimewa Yogyakarta
13,6 9,2 0,3
Jawa Timur 88,6 76,3 6,2
Banten 19,4 10,7 0,4
a. (Points: 10) Make a correlation matrix for the variables Number of Recovered and Number of Death. Interpret the results briefly. Write down the steps in full. Write down to two digits after the comma.
b. (Points: 15) By only looking at variables X1 and X3, if a province has 100,000 (one hundred thousand) positive cases, what is the predicted number of patients who die in that province? Write down the steps in full. Each calculation result, write up to two digits after the comma.
c. (Points: 20) By looking at the three variables X1, X2, and X3, and through the standardization process, calculate the Euclidean distance between the province of West Java and provinces other than West Java. If the provinces that will become one group are those with a distance of less than 2 (after standardization), which provinces will be in the same group as the province of West Java? Write down the steps in full.
Note: For number 2, you can use Ms. Excel or R to help the calculation process. The results of calculations with Ms. Excel and R remained handwritten.
3. Given a matrix 𝐴 = 06 7 7 84.
a. (Points: 10) Determine the eigenvalues for the matrix A. Write down the result of the calculation to two digits after the comma.
b. (Points: 15) Determine the unit eigenvectors for each of the eigenvalues you get in number a). Write down the result of the calculation to two digits after the comma.
c. (Points: 10) Calculate the dot product between the eigenvectors you get in number b).
d. (Points: 10) Calculate the angle formed between the eigenvectors you obtained in number b). Write down the result of the calculation to two digits after the comma.
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