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SPAL part 1

# SPAL part 1 - SISTEM PERSAMAAN ALJABAR LINEAR(SPAL...

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SISTEM PERSAMAAN ALJABAR LINEAR (SPAL) Dr.-rer.nat. Ir. Yuswan Muharam, M.T. Departemen Teknik Kimia Fakultas Teknik Universitas Indonesia

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SISTEM PERSAMAAN ALJABAR LINEAR (SPAL) SPAL : himpunan persamaan aljabar linier yang variabel- variabelnya hanya berpangkat satu (linier). variabel Konstanta/ koefisien ( VRK ) Pemisahan variabel
SISTEM PERSAMAAN ALJABAR LINEAR (SPAL) matriks imbuhan ( augmented matrix )

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SISTEM PERSAMAAN ALJABAR LINEAR (SPAL) Syarat solusi SPAL:
SOLUSI SPAL SECARA NUMERIS Metode langsung Berdasarkan operasi-operasi baris yang langsung diterapkan pada matriks SPAL, Contoh: Eliminasi Gauss, Eliminasi Gauss - Jordan , Dekomposisi LU, Solusi sistem Matriks TRIDIAGONAL Metode tak langsung Metode iteratif ( trial and error ) Contoh: Metode Jacobi , Metode Gauss Seidel , dan Metode SOR ( successive over relaxation ).

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ELIMINASI GAUSS Fasa eliminasi: Mengubah Ax = b menjadi Ux = c . dimana U = matriks segitiga atas Fasa substitusi balik ( back substitution ) Contoh:
ELIMINASI GAUSS

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SPAL part 1 - SISTEM PERSAMAAN ALJABAR LINEAR(SPAL...

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