Ejemplo Gauss Jordan

EJEMPLO DE MATRIZ MÉTODO GAUSS JORDÁN

2x1 + 6x2 + x3= 7
X1 + 2x2- x3= -1
5x1 + 7x2 – 4x3= 9

-2R1+R2
-5R1+R3
-2R1+R2
-5R1+R3
-1
7
9
-1
7
9
1 2-1
2 6 1
5 7 -4
1 2 -1
2 6 1
5 7 -4
7
1
9
7
1
9
2 6 1
12 -1
5 7 -4
2 6 1
1 2 -1
5 7 -4

R1-2
R1-2




½ R2½ R2
-1
9
14
-1
9
14
-1
7
9
-1
7
9
1 2 -1
2 6 1
5 7 -4
1 2 -1
2 6 1
57 -4
1 2 - 1
0 2 3
0 -3 1
1 2 - 1
0 2 3
0 -3 13R2+R3
3R2+R3



-1
9/2
5
-1
9/2
5
2/11R3
2/11R3
-1
9/2
55/2
-1
9/2
55/2
1 2 -1
0 1 3/2
00 1
1 2 -1
0 1 3/2
0 0 1
1 2 - 1
0 1 3/2
0 0 11/2
1 2 -1
0 1 3/2
0 0 11/2

-2R2+R1
-2R2+R1




X1=10
X2=-3
X3=5
X1=10
X2=-3
X3=5
4R3+R1-3/2R3+R2

4R3+R1
-3/2R3+R2

10
-3
5
10
-3
5
1 0 0
0 1 0
0 0 1
1 0 0
0 1 0
00 1
-10
9/2
5
-10
9/2
5
1 0 - 4
0 1 3/2
0 0 1
1 0 - 4
0 1 3/2
0 0 1