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Sistem Persamaan Linier

Sistem Persamaan Linier. SolusiTrivial x 1 =0,x 2 =0,..,x n =0. Konsisten. Solusi Nontrivial Solusi tak terhingga. Homogin. Tidak Konsisten. SPL. 1. Metode Cramer 2. Metode Invers 3. Metode Gauss 4. Metode Gauss- Jordan. Konsisten. Non Homogin. Tidak Konsisten.

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Sistem Persamaan Linier

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  1. SistemPersamaan Linier

  2. SolusiTrivial x1=0,x2=0,..,xn=0 Konsisten Solusi Nontrivial Solusi tak terhingga Homogin Tidak Konsisten SPL 1. Metode Cramer 2. Metode Invers 3. Metode Gauss 4. Metode Gauss- Jordan Konsisten Non Homogin Tidak Konsisten

  3. Sistem persamaan linear 3x1 – 7x2 + x3 = 0 -2x1 + 3x2 – 4x3 = 0 2x1 – x2 + 2x3 = 7 x1 + 3x2 – 5x3 = 0 - x1 + x3 = 4 Dng notasi matriks Dng notasi matriks = = A X = G A = G X Matriks augmented : matriks koefisien A ditambah matriks konstanta G. A, matriks koefisien X, matriks variabel /peubah G, matriks konstanta (A | G) =

  4. SISTEM PERSAMAAN LINEAR A X = G G = 0 ? tidak ya Sistem persamaan linear nonhomogen A X = G, dng G ≠ 0 Sistem persamaan linear homogen A X = 0 Contoh : Contoh : 2x + y – 7z = 0 3x + 2y + z = 5 x – 6y + 2z = 0 3x – 5y + 3z = 0 x + 2y – z = 0 2x + y + 2z = 0

  5. SPL homogin a11x1 + a12x2 + …….. + a1nxn = 0 a21x1 + a22x2 + …….. + a2nxn = 0 ……………………………………. ……………………………………. am1x1 + am2x2 + …….. + amnxn = 0 Contoh : x1 – 2x2 + 3x3 = 0 x1 + x2 + 2x3 = 0

  6. SPL non homogin a11x1 + a12x2 + ….+ a1nxn = b1 a21x1 + a22x2 + ….+ a2nxn = b2 ………………………………… ………………………………… am1x1 + am2x2 + ….+ amnxn = bm CONTOH x1 – 2x2 + 3x3 = 4 X1 + x2 + 2x3 = 5

  7. SPL HOMOGEN • Solusi Trivial • Solusi Non Trivial

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