Tentukan himpunan dari 2×+y+z=8 3×-y+2z=17 4×+2y-z=1

Tentukan himpunan dari 2×+y+z=8 3×-y+2z=17 4×+2y-z=1

2x + y + z = 8
3x – y + 2z = 17
4x + 2y – z = 1

| 2. 1. 1. |
| 3. -1. 2 | = D
| 4. 2. -1. |

D = 2 + 8 + 6 – (-4) – 8 – (-3) = 15

| 8. 1. 1. |
| 17. -1. 2 | = Dx
| 1. 2. -1. |

Dx = 8 + 2 + 34 – (-1) – 32 – (-17) = 30

| 2. 8. 1. |
| 3. 17. 2 | = Dy
| 4. 1. -1. |

Dy = -34 + 64 + 3 – 68 – 4 – (-24) = – 15

| 2. 1. 8. |
| 3. -1. 17 | = Dz
| 4. 2. 1. |

Dz = -2 + 68 + 48 – (-32) – 68 – 3 = 75

$x = frac{Dx}{D} = frac{30}{15} = 2$
$y= frac{Dy}{D} = frac{ - 15}{15} = - 1$
$z = frac{Dz}{D} = frac{75}{15} = 5$

x = 2

y = -1

z = 5

Semoga bermanfaat ^_^