Model Penyelesaian Determinan Matriks dengan Metode Eliminasi Gauss Melalui Matrix Laboratory (MATLAB)
DOI:
https://doi.org/10.32487/jst.v3i1.225Abstract
Abstract
Matrix determinant with the order 2 x 2 and 3 x 3 can be determined by certainly formula (Sarrus method). Nevertheless, that method can’t be used and applied to solve the biggest case such as matrix with order up on it. The Gauss eliminations method is used to finish the matrix determinant with the order 4 x 4 and 5 x 5 by using MATLAB. The calculation results show that the new matrix is produced by row operation elementary like that addition and subtraction between the row have the same determinant. The resulting new matrix determinant from the operation of the exchange between the rows of the matrix has the distinction of beginning so needs to be multiplied by -1. The number of -1 timer involved depending on the multiplicity of exchanges between the line that performed well in the initial matrix or matrix of operating results given.
Keywords : Model of solutions, Determinants, Matrix, MATLAB
Abstrak
Menentukan determinan matriks berordo 2 x 2 dan 3 x 3 dapat menggunakan rumus yang telah ditentukan (metode Sarrus). Walaupun demikian, metode tersebut tidak dapat digunakan dan diterapkan untuk memecahkan kasus yang lebih besar misalnya matriks yang berordo di atasnya. Metode eliminasi Gauss digunakan untuk menyelesaikan determinan matriks berordo 4 x 4 dan 5 x 5 dengan menggunakan MATLAB. Hasil perhitungan menunjukkan bahwa matriks baru yang dihasilkan dari operasi baris elementer seperti penjumlahan dan pengurangan antar baris memiliki determinan sama. Determinan matriks baru yang dihasilkan dari operasi pertukaran antar baris memiliki perbedaan dari matriks awal sehingga perlu dikalikan oleh -1. Banyaknya pengali -1 yang dilibatkan bergantung dari banyaknya pertukaran antar baris yang dilakukan baik pada matriks awal maupun matriks baru dari hasil operasi yang diberikan.
Kata kunci : Model Penyelesaian, Determinan, Matriks, MATLAB
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