Ecuaciones

Eliminacion Gaussiana.

x1+2x2+3x3 =9
4x1+5x2+6x3=24
3x1+x2+2x3=4

1 2 3 9 R2-4r1 1 2 3 9 R2 1 2 3 9 R3+5R2
4 5 6 24 R3-3R1 0-3-6 -12 -3 0 1 2 4
3 1 2 4 0-5-7 -23 0-5-7 -23

1 2 3 9 R3 1 2 3 9
0 1 2 4 3 0 1 2 4
0 0 3 -3 0 0 1 -1X1+2X2+3X3 = 9 X2+X(-1) = 4 X1+2(6)+3(-1) = 9
X2+2X3 = 4 X2 = 4+2 X1+12-3 = 9
X3 = -1 X2 = 6 X1 = 0

30x+40y+50z = 180
50x+50y+50z = 180
65x+40y+15z = 480

30 40 50 480 R1 1 4/3 5/3 16 R2-50R
50 50 50 480 30 50 50 50 480 R3-65R1
65 4015 480 65 40 15 480

0 4/3 5/3 16 -3 R2 1 4/3 5/3 16
0 -50/3 -100/3 -320 50 0 1 2 96/5
0 -140/3 -280/3 -560 0 -140/3 -280/3 -560

R1 -4/3 R2 1 0 -1 -48/5
R3+140/3 R2 0 1 2 96/5
0 0 0 336

X1 = -2.79
X2= 5.58
X3 = -2.79

Metodo de pivoteo.

X1-X2+X3 = 1
-3X1+2X3-3X3 = -6
2X1-5X2+4X3 = 5

1 -1 1 1 -3 2 -3 -6 (1/3) 1 -2/3 1 2 R1(-1)+R2 = NR2
-3 2 -3 -6 1 -1 1 1 1 -1 1 1 R1(-2)+R3 = NR3
2 -5 4 5 2 -5 4 5 2 -5 4 5

1 -2/3 1 2 1 -2/3 1 2 (-3/11) 1 -2/3 1 2
0 -1/30 -1 0 -11/3 2 1 R2 NR2 0 1 -6/11-3/11
0 -11/3 2 1 0 -1/3 0 -1 0 -1/3 0 -1

R2(1/3)+R3 1 -2/3 1 2 1 -2/3 1 2 (11/2)
0 1 -6/11 -3/11 0 1 -6/11 -3/11
0 0 -6/33 -12/11 0 0 -2/11-12/11

1 2/3 1 2 1 2/3 12 X1+2/3(3)-6+2
0 1 -6/4 -3/11 0 1 -6/113/4 X1=2-6+2=4-6=-2
0 0 1 -12/2 0 0 1 6 X1= -2

X2= -6/11(6) +/11 =33/11 = 3 X2 =3 X3=6

Metodo LU.

X1+2+3X3 = 1 (V1) 1 2 3 1 -4V1+V2 1 2 3 1
4X1+5X1+X3 = 2 (V2) 4 5 1 2 0 -3 -11 -2
6X1+2X2+X2 = 3 (V3) 6 2 1 3 6 21 3

1 2 3 1 -6V1+V3 1 2 3 1 -10/3 V2+V3 1 2 3 1
4 -3 11 -2 4 -3 11 -2 4 -3 -11 -2
6 2 1 3 6 -10 -17-3 6 10/3 59/311/3

1 0 0 1 2 3 1 1 2 3 X1 1
4 1 0 0-3 -11 -2 4 5 1 X2 = 2 _ _
6 10/3 1 0 0 59/3 11/3 6 2 1 X3 3 A=X=B

59/3 X3=11/3 V3 X3= 11/3 / 59/3 X3= 11/59
X1+2(-1/59)+3(11/59)=1 X2=(3)(1)/(59)(3) X2= 1/-59
X1=1-33/59+2/59
X1=1-31/59
X1=28/59

2da Forma.
x1+2x2+3x3 =9
4x1+5x2+6x3=24
3x1+x2+2x3=4

1 2 39 R2-4r1 1 2 3 9 R2 1 2 3 9 R3+5R2
4 5 6 24 R3-3R1 0-3-6 -12 -3 0 1 2 4
3 1 2 4 0-5-7 -23 0-5-7 -23

1 2 3 9 R3 1 2 3 9
0 1 2 4 3 0 1 2 4
0 0 3 -3 0 0 1 -1

(Ec1*-4)+E2 (Ec1*-3)+Ec3 Ec2/-3 (Ec2*5+E3)
-4 -8 -12 -36 -3 -6 -9 -27-3/-3 -6/-3 -12/-3 5 10 20
-4 5 6 24 3 1 2 4 1 2 4 -5 -7 -23
0 -3 -6 -12 0 -5 -7 -23 0 3 -3

-3x2-6x3=-12 -3x2+6=-12 3x3=-3 x1+2x2+3x3=9
-3x2-6(-1)=-12 -3x2=-12-6 x3=-3/3 x1+22(6)+3(-1)=9
-3x2=18 x3=-1 x1+12-3=9...