𝑮𝒂𝒖𝒔𝒔 𝒎𝒆𝒕𝒉𝒐𝒅

Solve:
｛ ２ｘ － ４ｙ ＋ ３ｚ ＝ ４； 
    ｘ － ２ｙ ＋ ｚ ＝ ３；
  ５ｘ ＋ ｙ ＋ ７ｘ ＝ １１ ｝ 
_____________________________________

2, -5, 3 | 4
1, -2, 1 | 3
5,  1, 7 | 11

L1º - 2·L2º 
L3º - 5·L2º

0, -1, 1 | -2
1, -2, 1 | 3
0, 11, 2 | -4

L3º - 2·L1º

0, -1, 1 | -2
1, -2, 1 | 3
0, 13, 0 | 0

 ｛ ｘ ＝ ５； ｙ ＝ ０； ｚ ＝ －２｝ 

 𝐒𝐨𝐥𝐯𝐞: 
{
 𝐱 - 𝟑𝐲 +  𝟕𝐳 =  𝟏𝟎 
𝟓𝐱 -  𝐲 +   𝐳 =   𝟖 
 𝐱 + 𝟒𝐲 - 𝟏𝟎𝐳 = -𝟏𝟏
} 
_____________________

1,-3,7,|10
5,-1,1|8
1,4,-10|-11

L2 := L2 - 5·L1
L3 := L3 - L1

1, -3, 7|10
0,14,-34|-42
0, 7,-17|-21

L2 = 2·L3
xL3

1, 0, -2/7 | 1
0, 1, -17/7|-3

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Indeterminado

 𝒙 - 2𝒛/7 = 1
 𝒚 - 17𝒛/7 = -3 

𝒙 = 1 + 2𝛂
𝒚 = -3 + 17𝛂
𝒛 = 7𝛂

Solve:
{
x1 - 3*x2 - 2*x3 = 7
2*x1 - x2 + 15*x3 = 3
x1 - 8*x2 - 21*x3 = 11
}

1,-3,-2|7
2,-1,15|3
1,-8,-21|11

R2 - 2 R1 → R2
R3 - 1 R1 → R3

1,-3,-2|7
0,5,19|-11
0,-5,-19|4

R3 + R2 → R3

1,-3,-2|7
0,5,19|-11
0,0,0|-7

𝑰𝒏𝒄𝒐𝒎𝒑𝒂𝒕𝒊𝒃𝒍𝒆