Bonsoir,
Méthode du pivot de Gauss :
3x + 4y + z = 2
x + 2y + z = 0
-x - 2y + 3z = 12
(3..4...1..|.2) ← L1
(1..2...1..| 0) ← L2
(-1...-2..3|12) ← L3
(3..4..1..|2) ← L1
(0..2...2.|-2) L2 ← 3L2 - L1
(0..-2..10|38) L3 ← 3L3 + L1
(3...4...1..|2) L1
(0... 2 ...2| -2) L2
(0...0...12|36..) L3 ← L3 + L2
ainsi z = 36/12 = 3
2y + 2×3 = -2
2y + 6 = -2
2y = -8
y = -8/2 = -4
3x + 4 × (-4) + 3 = 2
3x -16 + 3 = 2
3x - 13 = 2
3x = 15
x = 15/3 = 5
Conclusion : {x = 5 ; y = -4 ; z = 3}
