Soal
3x₁ + 2x₂ + x₃ = 5
x₁ + 2x₂ + 3 x₃ = 8
4x₁ + 5x₂ + 7 x₃ = 7
Penyelesaian :
ð 3x₁ + 2x₂ + x₃ = 5......…..…………persamaan (1)
x₁ + 2x₂ + 3 x₃ = 8…………………persamaan (2)
4x₁ + 5x₂ + 7 x₃ = 7………………… persamaan (3)
Persamaan (1) dan (2)
3x₁ + 2x₂ + x₃ = 5|x1| 3x₁ + 2x₂ + x₃ = 5
x₁ + 2x₂ + 3 x₃ = 8|x3| 3x₁ + 6x₂ + 9 x₃ = 24 _
-4x₂ - 8x₃ = -19
4x₂ + 8 x₃ = 19…………..persamaan (4)
Persamaan (1) dan (3)
3x₁ + 2x₂ + x₃ = 5|x4| = 12x₁ + 8x₂ + 4 x₃ = 20
4x₁ + 5x₂ + 7 x₃ = 7|x3| = 12x₁ + 15x₂ + 21 x₃ = 21 _
-7x₂ - 17 x₃ = -1
7x₂ + 17 x₃ = 1……..persamaan (5)
Persamaan (4) dan (5)
4x₂ + 8 x₃ = 19|x7| = 28x₂ + 56 x₃ = 133
7x₂ + 17 x₃ = 1|x4| = 28x₂ + 68 x₃ = 4 _
-12 x₃ = 129
x₃ = -10.75 ...... (x3)
Untuk Mencari Nilai X2 à Mengunakan nilai x₃
4x₂ + 8 x₃ = 19 .......Persamaan (4)
4x₂ + 8(-10.75) = 19
4x₂ - 86 = 19
4x₂ = 19 + 86
4x₂ = 105
x₂ = 26.25
Untuk Mencari Nilai X1 à Mengunakan nilai x₂ dan x₃
3x₁ + 2x₂ + x₃ = 5 .......... persamaan (1)
3x₁ + 2(26.25) -10.75 = 5
3x₁ + 52.5 – 10.75 = 5
3x₁ =5 - 52.5 + 10.75
3x₁ = - 36.75
x₁ = - 12.25
Jadi nilai x₁ = - 12.25
x₂ = 26.25
x₃ = -10.75
0 Response to " Soal Aljabar Linier & Matrix "
Post a Comment