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Determinan sebagai Penyelesaian Persamaan

Determinan sebagai Penyelesaian Persamaan. 1. SILABI. Cara determinan Penyelesaian persamaan linier dengan metode determinan Penyelesaian persamaan linier berganda dengan metode determinan. 2. Cara Determinan.

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Determinan sebagai Penyelesaian Persamaan

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  1. Determinan sebagai Penyelesaian Persamaan 1

  2. SILABI Cara determinan Penyelesaian persamaan linier dengan metode determinan Penyelesaian persamaan linier berganda dengan metode determinan 2

  3. Cara Determinan Cara determinan bisa digunakan untuk menyelesaikan persamaan yang jumlahnya banyak. Determinan secara umum dilambangkan dengan notasi Rumus determinan : ae - db 3

  4. Penyelesaian persamaan dengan Metode determinan Bila ada 2 persamaan : a1x + b1y = c1 a2x + b2y = c2 Maka penyelesaian untuk memperoleh nilai x dan y dapat dilakukan dengan : x = Dx y = Dy D D D = a1 b1 = a1b2 – a2.b1 a2 b2 Dx = c1 b1 = c1b2 – c2b1 c2 b2 Dy = a1 c1 = a1c1 - a2c2 a2 c2 4

  5. Contoh a b c x + y = 2 1 1 x 2 2x - y = -5 2 -1 y = -5 D = 1 1 = 1(-1) - 1(2) = -3 2 -1 Dx = 2 1 = 2 (-1) – (-5)1 = -2 + 5 = 3 -5 -1 Dy = 1 2 = -5 (1) – (4) = -9 2 -5 x = Dx = 3 = - 1 y = Dy = -9 = 3 D -3 D -3

  6. - - - + + + Penyelesaian persamaan linear berganda dengan determinan a1 b1 c1 a1 b1 D = a2 b2 c2 a2 b2 a3 b3 c3 a3 b3 (a1b2c3 +b1c2a3 + c1a2b3) – ( a3b2c1 + b3c2a1 + c3a2b1) d1 b1 c1 Dx Dx = d2 b2 c2 x= d3 b3 c3 D a1 d1 c1 Dy Dy = a2 d2 c2 y = a3 d3 c3 D Dz = a1 b1 d1 Dz a2 b2 d2 z = a3 b3 d3 D

  7. a b c d 1 -2 1 x -1 2 -3 4 y = -5 3 -1 2 z 1 x – 2y + z = -1 2x - 3y + 4z = -5 3x – 4y + 2z = 1 D = 1 -2 1 2 -3 4 3 -4 2 = (1)(-3)(2) + (-2)(4)(3) + (1)(2)(-4) - (3)(-3)(1) - (-4)(4)(1) - (2)(2)(-2) = (-6) + (-24) + (-8) - (-9) - (-16) - (-8) = -38 + 33 = -5

  8. Dx = -1 -2 1 -5 -3 4 = 6 + (-8) + 20 – (-3) - 16 -20 1 -4 2 = 18 - 33 = -15 x = Dx = -15 = 3 D -5 Dy = 1 -1 1 2 -5 4 = (-10) + (-12) + 2 – (-15) - 4 - (-4) 3 1 2 = -20 + 15 = -5 Y = Dy = -5 = 1 D -5 Dz = 1 -2 -1 2 -3 -5 = (-3) + 30 + 8 - 9 - 20 - (-4) 3 -4 1 = 35 - 25 = 10 z = 10 = -2 -5 HP = (3,1,-2)

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