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Ejercicios
- 1. METODOS DIRECTOS PARA SOLUCION DE SISTEMAS ECUACIONES LINEALES.
Eliminación de Gauss Simple:
2x−������ + ������=2
3������ + ������ − 2������ = 9
−x+2y+5z=−5
2 −1 1 2
3 1 −2 9
−1 2 5 −5
2 −1 1 2 2 −1 1 2
2R3+R1 3 1 −2 9 −2������2 + 3������1 0 −5 7 −12
0 3 11 −8 0 3 11 −8
2 −1 1 2 2 −1 1 2
5R3+3R2 0 −5 7 −12 R3/76 0 −5 7−12
0 0 76−76 0 0 1 −1
2 −1 0 3 2 −1 0 3
−R3+R1 0 −5 7−12 −7R3+R2 0 −5 0−5
0 0 1 −1 0 0 1−1
−10 0 0 −20 1 0 0 2
−5R1+R2 0 −5 0 −5 R1/−10 0 −5 0−5
0 0 1 −1 0 0 1−1
1 0 0 2
R2/−5 0 1 0 1
0 0 1−1
- 2. Descomposición LU
25 5 1
A= 8 12 6
9 18 3
25 5 1 25 5 1
R2−8/25������1 0 10.4 5.68 R3−9/25������1 0 10.4 5.68
9 18 3 0 16.2 2.64
Se halla U
25 5 1
R3−16.2/5������1 0 10.4 5.68 = ������
0 0 −0.6
Se halla L
22.4 0 0
L= −10 −24 0
9 18 3
Se despeja Y de L*Y
22.4 0 0 ������1 8
−10 −24 0 ∗ ������2 = 5
9 18 3 ������3 3
22.4Y1 =8
−10Y1 −24Y2 =5
9Y1 +18Y2 + 3Y3 =3
Y1=5/14
Y2=−5/14
Y3=29/14
- 3. Se despeja X de U*X
25 5 1 ������1 5/14
0 10.4 5.68 ∗ ������2 = −5/14
0 0 −0.6 ������3 29/14
25X1 + 5X2 + X3 = 5/14
10.4X2 + 5.68X3 =−5/14
−0.6X3= 29/14
X3=−3.5
X2=1.9
X1=−0.23