Matrix in Linear Algebra for Modern Computational Solutions
DOI:
https://doi.org/10.69533/wcv24y31Keywords:
Matrix, Vector, Linear Equations, Matrix Invers, Distance MatrixAbstract
This study aims to examine the basic concepts of matrix in linear algebra through conceptual and computational approaches. Matrix are understood not only as computational tools, but also as representations of linear transformations and relationships in vector spaces. The method used is a combination of theoretical analysis and numerical experiments using NumPy and SymPy. A case study was conducted by constructing a distance matrix between 20 districts in Cianjur in the form of a 20x20 symmetric matrix. The results show that the determinant of the matrix reflects the stability of the spatial system, while the inverse is useful for solving systems of linear equations. Eigenvalue and eigenvector analysis identified the most strategically located districts within the network. Additionally, the farthest distance between districts was successfully determined and can be utilized for more efficient transportation route planning. In conclusion, a conceptual and computational understanding of matrix structure is crucial, not only in linear algebra theory but also in practical applications such as regional planning and transportation network management.
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References
I. Handayani, W. Noviana, J. P. Glasser, S. P. Linear, and A. Pendahuluan, “Soal Aljabar Linear Dan Matriks,” pp. 63–69, 2022.
Nurhaswinda, N. U. Fitriah, A. F. Aini, and Z. Natasya, “Penerapan aljabar linear dalam pemodelan sistem dinamis,” Cahaya Pelita J. Pendidik. Dan Kebud., vol. 1, no. 2, pp. 82–85, 2025.
R. Cahyadi and N. Sutriningsih, “Analisis Penalaran Matematis Mahasiswa
Menyelesaikan Soal Matriks Proyeksi
Ortogonal Pada Matakuliah Aljabar Linear,” J. e-DuMath, vol. 8, no. 2, pp. 76–82, 2022, doi:
52657/je.v8i2.1803.
I. Maryati, Y. Suzana, D. Harefa, and I. T. Maulana, “Analisis Kemampuan Komunikasi
Matematis dalam Materi Aljabar Linier,”
Prisma, vol. 11, no. 1, p. 210, 2022, doi:
35194/jp.v11i1.2044.
R. C. &. N. Sutriningsih, "Analisis Penalaran Matematis Mahasiswa dalam Penyelesaian Soal Matriks," Jurnal e-DuMath, vol. 8, no. 2, pp. 76-82, 2022.
T. Hidayat, Komputasi Matriks dengan Python, Semarang: UNDIP Press, 2023.
R. F. d. D. A. T. Hidayat, "Implementasi NumPy untuk Analisis Matriks Transportasi," Jurnal Ilmu Komputer, vol. 4, no. 2, pp. 33-40, 2023.
Y. Suzana, Matriks dan Ruang Vektor, 2022: UNP Press, Padang.
T. H. &. L. Puspitasari, "Matriks untuk Sistem Navigasi Darurat," J. Ilmu Komp. UGM, vol. 15, no. 3, pp. 67-75, 2023.
B. Santoso, "Pemodelan Rute dengan Matriks Adgacency," J. Teknol. Inf., vol. 5, no. 1, pp. 22-30, 2024.
B. Santoso and A. S. H. Wijaya, "Penerapan Aljabar Linear dalam Analisis Komponen Utama untuk Data Kesehatan," Jurnal Statistika Indonesia, pp. 15(2), 45-60, 2021.
E. Prasetyo, "Komputasi Matriks dengan Python," J. Ilm. Komp., vol. 7, no. 2, pp. 101-110, 2022..
M. Rizal, "Aljabar Linear untuk Optimasi Rute," J. Mat. UNJ, vol. 6, no. 2, pp. 45-53, 2023..
S. Rahayu, "Analisis Eigenvector Centrality untuk Jaringan Jalan," J. Ilmu Komp, vol. 7, no. 1, pp. 22-30, 2023..
W. Noviana, Matriks dan Transformasi Linear., Surabaya: Unesa Press, 2023.
I. P. Hatoguan and I. M. Karo Karo, "KAJIAN KONSEPTUAL MATRIKS SEBAGAI STRUKTUR DASAR DALAM ALJABAR LINEAR," JATI (Jurnal Mahasiswa Teknik Informatika), vol. 9 , no. 3, pp. 5325-5329, 2025.
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