Metodos Numericos - Factorizacion Ecuaciones -Apk

194
DOCENTE: Ing. Saúl ARAUCO ESQUIVEL HUANC ROJAS CASTELLANOS JONIFER

description

métodos numéricos factorización de ecuaciones

Transcript of Metodos Numericos - Factorizacion Ecuaciones -Apk

Page 1: Metodos Numericos - Factorizacion Ecuaciones -Apk

DOCENTE:

Ing. Saúl ARAUCO ESQUIVEL

HUAN

CAYO

ROJAS CASTELLANOS JONIFER

Page 2: Metodos Numericos - Factorizacion Ecuaciones -Apk

A = randi(15,100,100);

Page 3: Metodos Numericos - Factorizacion Ecuaciones -Apk

disp('LA MATRIZ DE COEFICIENTES DEL SISTEMA DE ECUACIONES (MATRIZ A) ES:')disp(A);b=randi(100,100,1);disp('LA MATRIZ DE TERMINOS NO HOMOGENEOS (MATRIZ B) ES:')disp(b);[L,U,P]=lu(A);disp('LA MATRIZ "L" DEL SISTEMA ES:')disp(L);disp('LA MATRIZ "U" DEL SISTEMA ES:')disp(U);disp('LA MATRIZ "Y" DEL SISTEMA ES:')y=inv(L)*b;disp(y);x=inv(U)*y;disp('LA SOLUCIÓN DEL SISTEMA (X) es:')disp(x)

>> NUMEROSALEATORIOS

LA MATRIZ DE COEFICIENTES DEL SISTEMA DE ECUACIONES (MATRIZ A) ES:

Columns 1 through 15

13 3 10 1 7 9 13 9 11 15 10 12 8 7 8

14 12 6 11 2 9 9 13 2 3 6 11 8 11 10

2 5 13 1 9 14 14 6 11 4 15 1 14 15 13

14 8 8 2 8 4 11 7 2 6 4 13 6 13 8

10 3 6 8 11 5 9 1 2 2 10 14 7 8 4

2 10 15 2 11 2 13 3 10 11 10 12 15 12 7

5 4 14 13 10 15 14 10 5 7 6 1 1 7 7

9 10 9 13 1 10 15 5 10 15 3 6 15 15 15

15 11 10 11 2 8 1 14 12 7 1 11 3 15 10

15 12 9 3 5 10 13 2 9 10 7 11 11 13 11

3 7 4 10 8 9 10 15 12 3 3 4 9 6 11

15 2 5 8 10 10 15 9 4 6 11 5 11 7 6

15 4 8 15 7 9 8 11 12 3 6 11 6 4 8

8 14 4 10 13 11 8 15 15 12 13 8 10 12 9

13 3 13 13 11 8 13 5 14 14 12 10 13 14 3

3 13 3 7 15 15 4 7 2 6 9 4 1 14 9

7 9 4 7 8 4 8 7 6 11 3 3 2 9 11

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14 15 3 13 5 2 14 12 6 5 15 13 15 9 7

12 2 4 2 2 2 9 13 11 8 4 12 10 3 13

15 7 7 2 10 1 13 2 9 13 14 15 4 14 11

10 2 5 3 12 7 12 3 12 9 4 2 7 7 6

1 15 14 6 7 7 9 6 6 6 6 3 2 4 7

13 1 7 13 2 6 4 1 4 5 2 2 5 14 6

15 12 3 13 4 12 10 8 2 7 10 8 4 12 12

11 13 14 1 3 10 2 6 12 7 3 3 5 14 12

12 14 15 6 5 12 10 3 4 6 1 14 3 5 7

12 2 7 8 7 14 10 4 6 9 11 2 6 11 11

6 6 2 7 8 15 11 14 9 12 6 1 2 10 15

10 4 4 10 7 3 14 11 4 7 10 9 14 2 12

3 13 7 10 14 3 15 8 10 7 6 12 2 7 11

11 7 9 5 8 11 12 14 8 2 10 5 14 5 2

1 14 4 7 15 2 9 2 3 1 1 3 6 11 6

5 3 10 1 10 8 14 12 12 5 14 6 1 5 9

1 4 11 15 15 8 9 12 2 5 13 4 6 14 7

2 3 4 3 4 13 1 9 5 10 12 8 12 13 1

13 3 2 2 11 8 2 3 4 15 13 14 12 6 4

11 14 5 6 5 6 13 9 8 15 6 10 9 8 13

5 9 5 3 11 11 8 5 2 7 10 2 11 11 1

15 9 7 8 11 12 13 3 7 4 9 6 14 13 13

1 3 8 6 2 8 4 4 2 12 8 1 1 10 2

7 13 2 15 4 6 9 14 2 12 5 8 5 9 11

6 10 4 14 4 3 10 2 12 12 4 7 1 5 8

12 6 13 1 11 9 1 4 5 12 7 15 3 7 4

12 8 1 12 13 4 10 1 10 2 4 13 11 11 9

3 7 14 5 6 1 6 7 15 11 13 8 11 14 2

8 2 11 7 12 12 1 1 7 7 15 14 14 11 11

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7 4 8 9 11 4 8 14 11 4 1 3 9 1 9

10 2 9 15 1 7 3 3 12 2 9 6 2 11 1

11 3 4 7 10 11 2 2 7 13 2 14 14 7 1

12 4 7 15 6 6 4 5 10 3 13 14 13 7 3

5 7 15 5 14 12 3 7 2 3 15 11 5 2 1

11 1 9 11 1 6 3 2 15 10 2 10 9 13 7

10 14 8 10 7 11 1 15 3 14 15 6 15 5 13

3 15 4 9 7 11 10 5 4 8 1 15 11 4 10

2 8 8 11 7 7 5 5 12 11 11 2 13 6 8

8 8 10 10 12 1 9 1 8 3 12 11 7 6 13

15 6 11 3 5 5 11 5 12 15 9 10 8 9 2

6 14 6 2 12 7 8 1 6 9 14 13 9 9 14

9 6 6 15 8 5 9 8 5 11 14 6 5 6 2

4 2 15 3 1 3 7 12 1 1 10 12 12 6 8

12 12 1 1 3 13 2 10 11 13 3 13 8 8 3

4 6 14 9 11 7 8 2 7 12 4 5 10 10 9

8 4 14 14 8 14 13 2 7 2 3 9 5 15 1

11 7 12 11 3 6 14 12 10 8 1 15 3 11 12

14 2 2 3 6 12 5 14 1 5 2 9 8 7 13

15 2 4 6 10 6 4 9 5 9 10 5 6 13 14

9 15 6 7 3 13 9 2 12 6 15 10 12 3 15

3 15 11 15 12 12 10 13 11 7 6 6 12 1 8

3 9 3 3 4 6 7 6 2 3 7 12 11 2 5

4 1 11 13 14 4 4 5 2 4 15 7 3 3 2

13 4 2 10 5 12 15 12 2 1 15 8 1 5 8

4 6 10 6 12 15 2 1 1 14 11 11 9 5 9

13 13 8 3 3 5 2 1 7 10 15 15 5 1 12

4 1 12 7 5 11 3 11 10 14 12 5 15 9 2

14 1 11 8 2 7 3 10 11 3 6 13 15 2 10

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6 3 14 2 9 13 10 8 8 14 10 12 5 3 8

3 10 14 9 11 12 9 11 2 12 4 15 13 10 3

4 11 6 4 9 3 1 11 10 9 5 1 14 13 15

10 10 11 6 7 13 14 12 2 7 11 6 9 15 9

8 7 3 9 10 15 11 5 3 4 8 10 14 9 7

6 9 1 4 10 8 12 11 2 12 7 5 15 15 15

13 5 12 5 11 14 1 9 3 4 10 4 9 9 10

9 12 8 10 10 9 13 6 3 1 12 11 11 8 7

9 3 8 4 15 3 15 1 3 12 9 10 9 5 13

14 11 14 13 4 3 15 12 5 11 9 9 1 7 8

5 3 10 15 11 7 13 6 5 11 9 10 7 8 9

12 6 10 11 4 12 12 10 4 10 8 1 10 2 11

12 10 13 6 2 13 8 12 4 7 2 6 8 14 6

6 12 13 9 10 12 3 2 14 6 11 7 6 1 4

9 2 9 2 7 5 6 2 11 13 15 4 15 7 9

2 14 3 14 7 9 3 9 9 5 6 11 13 13 14

1 12 4 14 10 2 1 8 3 13 15 13 13 6 7

8 8 14 13 12 2 15 14 4 12 6 5 6 10 2

12 7 1 4 6 3 5 12 2 13 14 11 9 13 7

15 7 8 9 10 11 5 12 14 8 7 3 14 14 5

2 5 3 1 7 8 5 1 11 10 7 13 15 14 7

9 8 15 7 13 3 8 2 9 15 4 3 11 3 13

8 8 11 5 13 8 10 2 5 7 2 9 4 4 7

1 13 8 3 4 3 1 12 3 1 5 6 10 14 6

6 12 8 3 10 1 13 15 10 14 11 13 2 9 6

Columns 16 through 30

3 11 13 3 3 12 15 1 2 13 13 1 8 8 11

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4 7 9 3 12 14 9 13 13 3 11 9 9 8 6

2 11 15 5 6 4 15 8 11 2 8 15 1 15 15

7 4 1 14 7 2 11 11 12 13 5 5 10 6 2

4 1 9 8 3 4 8 4 10 10 11 13 14 2 4

5 8 5 7 13 6 10 9 8 1 6 10 2 4 13

7 5 13 3 10 5 14 11 5 14 9 12 7 11 2

2 15 3 15 12 14 3 15 10 8 14 12 5 13 8

8 14 7 7 13 1 6 7 2 9 13 1 15 15 13

11 6 6 13 2 9 15 2 3 10 14 5 10 4 12

4 1 13 10 15 3 7 1 1 12 15 10 4 12 3

12 11 11 6 8 13 10 10 15 13 13 8 2 9 7

2 13 4 14 12 3 14 12 15 6 1 15 9 7 6

6 15 5 12 12 8 15 11 2 2 1 12 13 8 8

1 1 3 7 13 15 10 6 8 12 2 9 13 8 9

4 7 11 13 3 6 2 15 10 5 4 5 13 10 3

1 9 9 14 7 1 1 8 5 13 1 4 4 12 14

3 11 3 7 10 4 10 15 12 6 7 14 9 5 10

3 11 3 6 14 6 9 2 9 13 6 7 14 2 3

5 10 8 9 13 6 15 4 7 3 9 13 2 13 9

3 11 14 14 14 4 12 12 5 2 14 2 13 6 14

3 6 9 11 9 15 10 14 12 14 5 13 14 12 12

9 9 1 6 9 11 8 12 14 1 6 1 4 3 11

14 2 1 12 13 15 4 5 11 11 13 14 2 2 7

15 1 13 15 1 7 15 3 7 12 6 14 8 14 4

4 15 7 9 14 15 9 13 15 7 3 8 13 14 9

8 5 6 9 7 1 1 12 4 6 8 2 8 15 4

6 9 12 5 1 10 11 5 8 15 13 3 7 13 5

8 15 6 2 12 13 8 4 15 6 6 11 8 1 14

4 3 8 3 3 4 1 5 5 7 11 13 2 9 14

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2 3 11 2 3 14 14 13 4 3 10 1 2 15 12

7 6 14 7 10 12 5 13 14 5 7 12 14 8 14

3 14 5 1 4 13 4 9 2 5 8 15 10 14 3

1 6 10 14 5 9 2 9 5 14 15 6 4 2 8

15 5 15 10 7 12 5 5 9 4 2 10 13 15 10

7 3 2 1 7 5 4 11 4 5 5 6 1 14 14

15 6 9 1 6 4 10 12 10 7 7 4 7 9 10

12 6 7 4 10 5 1 7 12 11 9 12 11 7 6

1 2 5 7 3 9 5 7 8 3 14 11 6 6 12

11 7 4 2 3 13 5 7 10 14 8 5 7 11 13

11 2 12 1 2 5 14 5 12 2 7 9 8 1 10

10 10 15 11 5 7 7 11 4 7 12 7 14 6 2

9 1 3 6 12 13 12 14 10 1 8 2 12 14 14

4 9 12 12 4 10 10 14 2 12 13 1 2 9 1

12 12 3 7 12 15 12 12 8 11 7 8 5 8 8

4 4 15 7 11 4 2 4 13 4 8 5 6 8 2

6 7 13 1 13 13 15 11 14 11 8 6 13 5 6

14 9 7 1 13 11 13 2 8 9 4 5 7 15 13

13 1 11 2 5 4 1 2 5 13 2 3 4 15 4

7 8 8 9 5 8 7 3 10 9 2 6 9 8 14

5 10 13 4 8 6 5 3 14 14 14 11 8 15 11

10 4 6 13 5 9 10 9 8 7 4 4 14 7 6

14 13 2 13 13 13 4 2 15 6 13 10 15 7 4

14 15 9 15 13 2 9 13 3 8 11 7 13 4 4

9 13 14 8 9 13 10 11 2 4 14 7 11 3 12

5 8 3 4 4 13 9 14 5 14 15 3 12 13 1

13 5 7 4 11 6 7 8 6 8 3 3 14 11 11

7 12 12 9 4 7 1 10 7 4 6 10 1 8 10

14 4 1 12 7 9 8 14 5 7 15 5 6 13 12

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1 15 15 6 6 11 7 9 11 11 10 9 1 8 15

8 10 12 7 9 12 2 5 2 7 14 15 13 9 6

11 10 9 10 15 12 7 15 7 3 8 11 8 4 4

3 3 3 14 12 6 7 1 5 13 1 11 6 9 14

6 2 8 3 15 7 9 5 5 9 10 15 4 3 13

3 4 8 11 4 15 13 15 2 6 4 12 9 1 7

5 13 15 9 8 9 11 6 9 4 8 10 5 11 2

7 14 13 7 1 13 14 5 5 4 11 15 2 10 9

9 11 15 14 12 5 1 2 3 8 10 1 2 4 3

1 11 11 6 10 10 4 14 1 7 9 5 2 7 8

9 4 7 3 13 9 7 3 5 12 7 15 7 10 6

5 9 15 10 15 15 15 5 9 2 4 12 2 9 5

4 13 8 10 14 2 12 14 14 13 7 8 7 2 11

4 7 4 5 7 8 7 8 1 11 1 11 14 3 8

3 15 6 13 1 8 6 10 14 3 10 7 6 1 12

15 2 11 15 9 2 1 9 2 13 15 6 2 7 4

15 5 9 15 4 14 12 11 13 3 2 4 9 8 11

13 8 12 2 4 14 8 1 13 10 1 6 14 3 1

11 1 15 4 5 7 3 8 14 9 14 1 6 11 13

3 11 15 1 2 12 7 1 3 3 4 8 1 1 11

6 9 9 10 12 3 3 13 8 1 1 6 3 2 15

3 8 15 2 12 10 12 6 7 12 13 15 2 15 2

1 13 2 7 9 4 6 13 3 12 3 9 12 15 14

5 13 1 14 6 7 15 4 9 7 14 13 7 1 8

11 12 5 9 13 13 1 9 10 1 2 7 11 8 10

10 5 9 6 9 3 13 15 4 9 6 7 11 13 5

9 7 8 4 15 5 10 1 8 3 9 13 9 4 2

7 12 14 7 14 8 9 1 15 11 9 15 10 13 13

5 2 9 15 6 6 10 1 8 9 11 8 14 13 3

Page 10: Metodos Numericos - Factorizacion Ecuaciones -Apk

8 2 7 2 9 12 11 11 11 4 10 14 10 10 6

12 5 9 8 6 15 2 9 7 14 7 12 14 1 10

12 8 11 13 10 3 14 2 1 12 3 9 8 6 15

9 15 1 1 12 4 1 12 5 14 12 15 3 14 8

12 11 13 11 12 11 5 10 13 2 4 13 2 11 15

10 5 3 15 2 6 3 2 6 3 10 15 11 6 4

2 5 8 5 13 15 14 2 2 12 13 10 5 10 6

8 13 4 3 1 15 2 3 8 11 2 6 11 4 11

6 14 6 11 7 10 9 12 6 12 15 8 10 9 1

2 10 10 14 11 13 10 2 12 8 1 14 8 15 12

3 4 3 10 12 7 10 4 8 7 13 1 11 13 7

3 2 5 14 6 10 13 4 13 10 13 3 8 5 13

Columns 31 through 45

6 15 4 9 11 12 14 13 10 13 7 14 2 8 12

5 9 6 7 3 2 10 13 15 14 15 13 6 2 13

15 4 7 2 7 3 11 13 10 3 11 2 11 5 4

11 9 13 11 8 6 12 6 10 10 9 7 6 14 8

7 14 13 10 8 13 6 6 14 15 9 2 13 13 7

2 14 7 12 13 9 4 13 9 15 11 9 5 1 6

12 8 6 9 11 9 1 7 6 2 1 15 3 10 13

10 7 14 13 13 14 8 9 15 3 12 4 11 13 15

2 5 12 9 8 9 10 11 7 12 14 15 4 4 10

2 1 12 15 15 1 5 15 10 1 1 6 14 1 3

15 12 15 14 2 13 8 9 11 2 13 4 12 4 2

8 2 8 8 9 10 4 10 11 8 12 10 7 2 9

1 6 12 12 5 8 5 9 4 13 15 15 1 8 5

1 6 7 8 8 5 10 14 2 15 4 10 3 7 5

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3 14 13 13 11 4 14 13 5 1 14 1 5 6 9

14 1 6 5 4 8 13 3 14 9 10 6 14 14 3

7 13 12 15 10 4 4 3 9 13 2 3 10 7 11

9 5 15 5 5 1 6 4 7 14 5 4 5 5 1

8 4 8 2 14 3 14 12 7 13 12 1 5 1 1

2 8 7 12 3 4 4 3 12 14 13 14 7 4 5

14 11 4 13 2 3 15 15 10 12 2 12 14 4 2

5 4 5 14 15 10 10 11 10 2 8 6 14 1 14

5 4 2 5 3 13 3 3 3 8 4 13 8 11 13

9 15 6 13 3 13 13 13 7 3 14 12 10 1 6

8 9 5 9 3 13 10 14 8 13 5 10 11 10 3

6 5 6 7 2 11 9 15 6 14 13 6 1 7 7

10 15 13 13 7 13 4 9 8 3 4 6 9 4 7

15 14 8 15 11 12 1 9 6 14 14 2 1 10 11

10 3 8 2 13 4 4 3 12 6 3 6 7 5 7

5 1 12 11 12 15 6 8 6 6 12 9 8 2 15

4 11 2 4 11 2 10 9 11 5 1 7 1 9 14

7 14 10 6 8 10 15 3 8 14 10 10 1 3 15

1 2 6 5 11 4 4 8 11 12 9 8 14 14 6

14 1 6 13 15 4 12 9 15 7 6 13 9 10 5

10 9 9 15 8 6 14 3 8 11 4 2 6 13 14

4 10 13 10 5 3 8 10 14 15 12 7 6 12 4

8 8 3 11 12 8 3 1 4 3 3 9 3 13 2

1 1 11 14 4 15 13 5 14 4 8 3 3 10 8

13 11 14 11 4 6 8 8 2 10 1 10 6 11 14

7 15 3 9 7 9 2 5 7 13 3 1 6 11 7

9 14 5 6 10 10 14 10 1 13 8 9 12 5 4

9 2 8 10 10 11 10 6 13 6 13 13 8 8 2

11 6 14 6 2 7 2 3 3 2 3 8 7 14 14

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6 4 8 7 2 13 14 14 3 2 11 7 2 1 10

2 9 5 6 5 14 1 10 3 6 11 3 14 8 6

7 10 9 8 12 12 1 10 11 13 1 1 11 7 10

1 5 9 8 7 5 15 11 4 4 8 12 13 14 12

12 12 7 14 13 12 11 12 5 12 15 12 10 10 6

1 12 1 4 15 3 6 13 12 10 2 5 15 15 11

15 12 11 6 6 8 8 8 8 1 12 2 15 9 4

12 6 8 9 1 10 12 3 14 12 10 6 4 13 15

15 1 6 8 9 11 1 6 1 14 9 13 10 8 11

8 11 1 4 12 6 11 13 7 8 8 13 11 9 3

4 15 6 9 5 11 11 3 9 13 9 10 8 3 7

4 3 4 14 8 14 7 5 9 2 7 15 13 10 10

12 2 4 1 4 1 9 15 13 12 2 15 3 15 14

15 14 13 7 15 3 6 13 2 14 5 2 2 9 8

6 8 6 2 8 13 3 4 5 13 9 10 1 8 10

12 13 1 9 9 7 6 15 1 4 10 8 3 12 11

2 13 6 9 4 7 14 1 15 4 14 1 9 2 14

9 3 12 12 2 15 4 7 12 8 15 14 8 14 3

7 4 3 4 1 12 6 7 12 6 2 8 6 1 7

11 1 14 9 13 15 5 7 3 8 10 12 5 8 5

4 10 5 7 12 4 2 2 6 15 10 1 1 11 11

2 12 5 13 3 2 8 7 3 10 8 4 13 9 14

7 8 4 10 14 6 13 10 8 15 6 10 10 8 8

10 1 12 6 11 8 14 15 13 8 8 3 7 5 13

2 15 2 6 10 9 11 4 10 7 11 10 4 10 5

7 8 15 4 15 15 6 6 11 12 15 6 13 14 9

10 5 3 15 1 8 5 4 10 12 2 12 13 11 6

13 3 5 5 7 7 11 5 11 7 12 10 13 15 14

5 10 11 3 8 15 14 3 13 1 9 6 8 2 11

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7 9 3 6 9 4 14 1 10 2 14 5 15 8 13

14 12 8 12 2 10 2 7 3 12 2 6 13 2 2

11 3 11 11 10 15 8 4 9 10 5 14 2 9 5

4 6 14 11 1 11 2 14 3 1 1 7 4 11 12

12 3 11 1 9 5 4 8 14 9 8 7 13 3 4

5 13 12 6 11 8 14 14 2 11 12 7 7 12 1

5 6 7 14 8 1 3 15 6 2 5 15 7 6 7

1 5 4 5 10 14 2 9 9 4 4 4 15 14 15

6 1 8 9 4 7 9 2 8 13 5 14 15 5 4

7 13 4 5 10 5 5 14 13 3 7 1 12 1 9

5 8 13 2 6 15 6 9 8 14 12 6 9 4 6

5 9 10 6 2 7 12 14 4 14 8 12 14 2 1

4 14 13 13 6 5 13 7 11 1 6 6 8 15 8

15 11 12 15 4 2 11 10 3 6 14 10 3 1 13

13 11 8 13 4 9 7 2 10 3 15 7 5 2 4

6 3 5 2 10 3 10 14 10 9 10 1 5 1 1

8 9 11 6 8 2 4 10 4 2 2 9 9 4 4

9 15 15 4 7 9 10 2 3 1 10 10 2 1 10

8 9 12 5 4 5 11 11 3 14 6 10 2 10 5

5 13 13 15 13 6 10 6 3 15 15 6 3 8 10

15 15 11 9 13 11 6 2 4 6 5 8 15 4 1

3 14 9 12 5 13 6 4 15 10 11 11 13 3 11

13 4 12 13 10 6 3 4 1 2 9 14 11 2 6

1 1 8 3 12 15 12 4 15 4 3 1 15 6 1

5 7 13 14 15 15 8 11 1 1 11 2 15 1 7

12 1 2 2 14 4 6 12 15 8 1 10 15 10 11

10 8 15 12 6 12 12 9 5 3 3 12 3 8 14

3 15 2 11 3 10 4 9 8 15 1 15 15 5 15

Page 14: Metodos Numericos - Factorizacion Ecuaciones -Apk

Columns 46 through 60

15 5 1 7 11 3 2 7 7 5 11 12 12 10 5

14 1 15 10 15 12 1 5 1 10 5 8 14 12 7

13 2 8 3 14 8 10 3 6 5 9 6 8 1 5

13 12 14 8 2 10 1 3 6 12 3 1 13 13 12

9 11 6 10 15 15 3 13 5 12 7 4 9 6 6

7 12 14 1 3 5 11 8 13 15 1 9 12 6 2

2 10 4 8 15 2 8 15 7 7 4 7 1 5 10

10 13 14 14 9 12 9 15 13 7 4 14 8 9 6

13 1 14 2 4 6 13 7 12 9 8 1 4 5 6

5 7 6 7 2 9 12 6 5 13 4 7 5 6 2

13 4 10 10 5 3 8 4 2 1 6 9 15 6 14

2 8 9 5 13 2 5 7 1 3 12 3 4 10 7

6 14 14 15 2 3 2 4 10 15 7 9 8 10 2

5 5 4 11 6 13 14 7 7 15 1 13 4 15 14

3 9 1 4 2 5 15 7 14 7 6 3 9 15 5

10 1 14 9 3 6 15 4 7 13 8 3 15 6 10

5 3 4 14 1 10 10 3 3 14 13 1 2 3 10

15 13 4 9 11 13 2 7 9 11 5 10 15 14 4

8 3 10 12 2 12 2 8 15 6 13 1 2 5 15

12 13 5 14 10 6 3 5 10 7 9 5 3 9 10

1 6 13 13 3 3 1 11 6 7 1 15 10 14 9

10 11 14 2 10 10 11 7 4 11 4 12 2 2 14

9 1 15 3 8 1 3 7 13 7 9 4 2 4 9

13 12 6 3 5 5 10 12 15 15 8 11 10 7 1

10 8 13 1 13 10 12 13 6 6 3 3 1 9 8

14 15 3 1 13 9 9 12 2 6 4 10 15 14 13

14 5 10 9 15 5 6 12 3 14 12 13 9 4 12

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3 6 11 10 1 15 13 8 9 9 10 14 6 15 9

3 2 2 14 10 2 5 9 3 12 3 6 11 7 1

12 15 8 12 1 12 5 10 5 2 11 8 15 12 11

1 7 14 5 2 3 12 2 7 7 7 11 6 8 7

6 2 4 8 2 7 8 4 6 2 7 11 11 5 10

5 11 4 4 6 13 4 10 5 10 11 7 10 7 12

12 8 13 11 4 6 11 5 7 11 7 6 12 11 13

2 5 8 2 6 2 3 12 4 14 1 5 9 14 1

12 12 3 12 4 9 14 5 1 10 2 2 6 14 12

12 13 4 13 6 5 4 1 10 11 9 7 13 3 9

8 4 10 12 7 2 2 5 3 13 7 3 4 2 2

4 9 9 6 10 11 2 9 13 8 14 6 12 14 4

2 7 5 9 12 8 12 15 7 7 2 14 15 10 3

10 3 10 8 5 3 13 11 5 13 6 8 5 1 9

1 10 11 2 13 2 12 11 12 13 9 14 11 8 9

1 15 5 13 12 4 12 9 12 3 2 2 10 14 2

2 2 7 11 13 3 15 9 3 1 14 15 7 6 15

7 14 6 5 3 5 7 14 2 1 10 2 8 5 4

11 9 12 15 1 15 12 6 3 3 14 5 15 4 5

13 7 3 3 10 8 7 7 10 3 10 12 15 4 5

8 3 14 5 11 4 15 4 13 10 1 10 11 6 1

1 4 5 7 2 7 1 12 8 1 5 7 6 9 8

5 7 8 4 2 11 15 9 3 8 2 5 1 5 4

10 8 12 3 9 9 9 6 11 11 10 2 9 10 7

12 6 11 11 13 10 6 11 14 2 1 5 9 13 15

5 12 3 3 13 13 9 2 4 4 11 3 6 2 14

8 14 11 8 2 6 5 1 14 5 8 5 14 11 2

13 12 2 5 11 12 3 9 4 3 5 2 10 10 9

9 7 15 7 14 3 10 10 13 5 8 13 10 8 6

Page 16: Metodos Numericos - Factorizacion Ecuaciones -Apk

9 10 14 14 7 1 11 9 13 13 11 15 5 14 11

5 10 8 4 2 6 12 14 8 5 13 4 2 2 8

7 2 11 1 4 13 6 10 8 12 5 11 5 9 4

12 8 15 14 11 6 4 8 14 9 5 1 4 4 8

6 5 2 11 1 15 6 4 1 9 6 10 6 1 13

7 9 12 8 7 10 5 1 8 11 10 11 13 9 11

6 15 13 8 9 6 14 11 10 12 13 1 3 13 3

11 7 12 2 15 14 12 3 12 14 12 1 3 9 3

9 1 3 15 4 14 5 5 4 3 14 3 8 13 6

10 14 7 6 2 13 10 4 1 12 14 13 10 4 13

8 14 1 10 10 4 12 9 3 3 3 5 3 10 11

6 6 5 6 2 5 13 9 12 1 13 8 10 3 10

8 4 3 1 15 12 14 12 15 2 15 8 13 5 3

1 12 7 9 4 11 9 14 6 3 12 9 12 1 2

7 8 9 8 10 8 2 12 15 2 14 5 4 11 14

15 9 12 4 13 15 4 15 5 15 2 7 5 15 7

12 11 7 1 13 8 14 3 3 5 10 7 3 12 8

11 2 8 13 8 15 7 14 6 15 5 15 7 12 7

12 14 14 1 12 8 10 1 9 10 10 1 5 9 8

12 15 14 5 14 8 12 4 10 14 14 6 5 5 5

13 2 9 12 14 12 4 1 9 6 6 12 14 4 4

12 13 14 15 4 6 9 11 5 4 12 9 6 5 14

15 14 1 9 9 7 4 14 3 3 3 5 6 15 14

2 1 13 12 12 2 1 9 3 9 8 14 9 4 10

6 8 6 11 3 12 12 3 3 4 10 2 2 9 6

8 10 4 10 12 9 1 8 11 5 11 5 4 4 9

4 6 13 10 8 10 6 9 7 1 5 14 11 7 11

1 10 6 15 9 12 4 3 2 9 4 10 9 3 14

15 12 3 9 4 4 4 5 11 15 14 11 4 6 2

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11 9 1 6 2 13 10 11 3 13 10 8 13 12 9

3 10 15 11 5 14 14 9 13 1 2 3 7 13 7

3 5 11 7 14 5 1 3 8 10 10 15 9 14 10

11 13 13 2 8 11 12 6 9 6 3 14 8 9 9

6 7 15 7 5 6 12 6 4 2 12 7 3 13 4

2 10 11 9 12 5 14 9 12 9 13 13 2 11 2

7 13 14 6 12 3 15 1 8 7 6 5 7 1 1

3 5 4 6 1 10 2 9 9 8 3 6 1 3 1

12 7 14 12 14 9 8 14 7 14 12 12 7 4 5

14 9 14 8 12 13 13 2 11 3 5 2 9 4 12

1 7 5 8 5 5 10 11 2 7 4 15 10 3 6

10 2 2 2 11 3 15 15 9 1 4 1 1 4 10

11 12 12 4 5 7 15 10 13 6 2 5 11 5 15

4 1 2 7 14 8 15 11 7 11 9 1 3 15 10

13 7 11 10 5 12 2 5 10 2 7 7 9 6 9

Columns 61 through 75

4 8 9 4 8 10 6 9 10 8 12 15 14 12 5

12 1 9 4 10 5 4 10 3 12 11 12 6 3 15

14 4 11 10 1 5 8 8 11 6 14 12 11 1 8

13 2 14 11 9 3 1 1 10 10 9 1 4 11 12

9 2 15 13 12 6 13 8 1 5 10 2 1 8 11

10 14 14 1 10 14 4 1 12 5 2 4 10 8 12

14 1 10 4 8 14 11 13 15 10 4 14 11 5 5

7 13 14 8 13 6 12 9 7 7 1 15 5 5 5

5 8 2 6 15 11 11 11 6 2 7 15 9 14 11

10 2 6 6 5 4 10 10 1 4 5 6 5 7 3

5 8 1 1 12 15 4 10 4 15 5 5 13 12 13

Page 18: Metodos Numericos - Factorizacion Ecuaciones -Apk

10 9 9 12 5 10 8 15 9 11 8 3 6 3 3

1 2 12 7 1 4 15 3 10 10 3 12 11 2 15

15 15 3 11 2 2 4 8 4 5 15 11 10 4 11

4 10 7 9 5 9 4 13 10 1 15 3 15 9 3

10 7 2 1 5 5 5 8 1 9 9 7 4 10 13

6 13 5 5 1 2 12 12 15 1 1 1 9 15 14

11 4 12 15 3 3 5 3 2 4 14 10 2 1 9

1 13 9 14 7 1 10 11 6 3 11 12 9 3 6

2 5 12 6 12 11 3 14 10 7 2 13 13 7 7

14 15 10 10 11 12 2 3 8 12 15 12 1 5 11

2 4 14 9 11 13 5 7 8 10 5 7 5 2 4

5 15 1 13 7 4 4 1 6 5 13 6 11 13 1

8 8 3 15 14 14 14 4 12 5 7 1 13 6 15

4 9 7 2 15 10 15 10 5 2 9 13 8 10 15

9 15 12 14 14 1 1 14 10 3 8 2 15 9 12

12 12 14 9 7 6 9 6 14 11 9 1 7 1 15

8 5 1 3 14 9 1 1 5 2 3 5 5 10 8

14 1 3 4 6 10 7 14 13 14 9 15 8 5 2

3 1 7 11 10 7 8 8 12 7 3 11 3 4 7

7 13 12 9 9 13 13 14 2 2 7 6 3 7 12

5 7 8 9 13 3 10 5 3 9 9 13 5 10 11

9 6 12 15 5 15 4 11 7 13 7 11 12 13 14

1 8 3 9 10 13 14 1 11 6 13 10 10 9 12

1 14 11 2 10 6 12 8 10 12 15 7 15 1 10

5 7 10 3 10 10 9 5 11 11 15 15 12 12 5

2 10 1 2 5 5 14 6 1 9 12 13 9 5 6

3 2 12 3 5 2 6 15 2 6 3 1 7 13 13

6 6 15 11 3 8 6 12 12 6 1 3 5 11 6

1 3 2 10 2 13 10 6 13 7 3 8 12 10 2

Page 19: Metodos Numericos - Factorizacion Ecuaciones -Apk

11 4 6 6 5 12 2 10 12 7 9 9 2 6 13

10 6 3 3 6 15 6 7 15 4 10 5 2 1 7

3 5 11 6 9 6 3 9 14 8 6 7 12 15 3

1 4 3 12 15 6 13 15 4 1 10 6 6 10 1

7 10 15 6 1 3 11 10 8 9 14 3 9 4 10

7 12 1 12 11 6 11 3 12 1 4 15 5 2 6

4 4 1 5 14 9 14 13 8 14 5 6 11 4 6

14 14 13 10 13 9 13 11 10 13 2 13 6 14 7

9 12 13 14 2 3 9 2 9 6 8 1 11 4 8

1 9 9 4 15 2 1 3 11 15 13 7 15 8 5

14 15 12 8 7 6 2 5 1 15 5 2 2 14 8

7 9 8 2 14 13 8 7 8 15 12 5 8 3 1

1 4 9 2 13 3 15 8 4 3 7 15 2 7 3

2 13 3 1 6 8 13 5 6 1 9 13 11 10 5

15 13 8 2 10 2 15 13 9 4 15 3 14 9 12

13 5 1 10 13 13 15 12 12 6 11 9 2 10 9

10 5 1 7 1 12 6 5 7 4 15 5 8 5 11

1 13 6 10 2 9 5 10 8 12 2 14 9 7 13

5 8 10 13 6 6 12 2 2 4 14 2 11 12 13

7 1 14 12 3 8 4 11 4 7 1 12 5 14 2

2 12 11 15 1 14 15 6 5 4 2 3 10 8 10

9 7 11 12 12 14 14 11 7 6 10 11 3 5 12

5 5 11 15 5 8 6 5 4 14 6 4 10 7 11

7 6 12 12 13 8 6 11 4 1 5 4 11 5 10

9 6 10 4 3 14 11 6 14 2 12 4 7 5 1

2 12 8 11 11 9 11 6 9 6 5 15 3 3 3

1 1 5 11 14 12 13 4 15 13 10 6 7 3 5

5 11 15 12 12 10 9 11 10 4 7 10 9 8 10

8 14 4 12 4 8 2 13 4 15 5 1 5 2 4

Page 20: Metodos Numericos - Factorizacion Ecuaciones -Apk

9 5 8 5 6 4 9 14 2 15 13 4 13 14 2

4 10 12 8 6 10 1 8 9 6 9 14 2 3 15

14 4 4 12 5 3 12 3 7 15 2 7 4 3 4

13 10 13 9 6 3 10 10 11 2 4 1 15 11 15

7 2 9 15 2 13 9 3 12 12 3 7 10 11 10

15 15 14 3 7 2 4 7 6 9 9 13 12 6 4

9 10 6 14 7 10 11 13 9 10 4 14 13 2 8

4 6 15 12 1 7 11 7 4 8 8 5 1 1 11

13 1 14 5 10 10 6 14 15 4 11 4 7 6 4

7 13 9 10 1 12 1 6 8 3 15 13 11 12 2

4 10 2 7 3 5 13 11 5 10 12 7 3 7 9

15 13 6 2 11 1 12 9 4 13 2 8 10 2 4

3 8 5 9 9 13 8 2 15 11 15 3 4 13 5

8 1 4 15 1 6 11 7 11 8 15 3 13 10 15

15 14 4 7 5 10 12 14 11 15 10 14 13 7 5

10 7 1 9 6 14 5 1 10 9 15 15 7 9 15

10 11 14 2 3 5 14 6 12 4 5 6 6 8 7

8 3 7 3 2 15 9 4 9 11 14 13 15 10 1

9 13 9 3 7 13 5 4 8 5 1 15 1 10 5

14 14 5 1 6 12 5 6 14 12 8 14 6 3 3

6 12 15 5 13 10 14 14 6 15 3 13 8 13 15

4 12 15 4 9 9 6 8 4 5 5 11 10 3 7

7 7 15 6 13 6 3 13 5 14 3 3 2 7 9

5 11 10 3 7 13 15 6 14 11 9 4 3 4 4

7 9 11 15 1 9 10 7 11 2 10 7 10 5 14

10 9 6 8 1 12 15 15 13 4 6 1 4 1 2

9 6 8 6 3 15 3 2 6 15 1 5 2 14 13

6 11 5 4 6 12 13 2 10 8 1 15 1 8 7

14 3 11 6 11 13 8 11 1 14 1 5 3 7 14

Page 21: Metodos Numericos - Factorizacion Ecuaciones -Apk

5 1 12 6 3 8 9 14 14 12 2 9 8 8 8

7 9 2 14 5 14 1 2 8 1 1 10 14 6 14

Columns 76 through 90

6 1 11 6 10 11 4 1 12 11 7 10 2 15 5

7 11 8 7 10 8 11 11 10 1 5 14 7 13 2

9 13 2 12 8 1 10 14 15 6 10 10 7 3 6

14 2 7 3 3 2 11 7 3 8 6 8 10 10 4

2 8 7 10 8 2 13 10 10 12 2 9 2 1 10

1 6 10 14 12 10 11 9 5 3 15 15 9 3 12

7 12 4 10 7 4 1 4 2 8 8 8 2 3 7

9 5 2 1 12 3 9 12 14 2 8 6 2 10 10

14 13 8 11 11 8 14 5 9 12 5 15 7 13 5

5 3 11 4 15 14 2 14 5 6 3 15 5 13 8

9 13 10 11 5 10 9 5 3 4 13 14 15 8 5

12 14 14 6 6 11 14 9 6 2 5 12 8 12 13

5 3 4 9 6 4 3 6 2 2 9 10 7 5 12

2 1 4 4 1 4 8 4 10 14 9 12 5 15 3

7 9 4 14 10 1 2 9 4 4 15 7 8 15 2

1 1 13 6 9 10 12 2 12 15 5 6 12 2 8

11 13 11 2 6 8 5 3 5 6 4 4 3 5 12

2 14 14 1 7 8 3 2 7 15 5 14 1 5 13

3 11 11 10 7 13 15 5 1 6 9 15 11 4 11

8 4 10 15 5 15 11 13 1 1 6 15 10 12 14

10 9 7 5 4 12 13 8 3 10 4 2 7 6 3

6 15 9 12 2 4 11 13 5 9 11 1 14 3 4

10 14 15 5 3 11 11 15 1 14 4 3 8 3 14

13 10 15 2 15 12 8 5 6 4 15 8 14 14 7

Page 22: Metodos Numericos - Factorizacion Ecuaciones -Apk

11 12 6 8 8 9 3 4 1 12 8 2 8 15 3

6 13 3 6 12 13 8 8 2 6 7 1 14 8 11

9 9 7 15 5 14 9 6 2 15 9 2 11 1 14

4 1 9 5 1 10 13 13 14 13 10 10 11 7 12

11 4 1 9 10 1 4 4 5 11 13 1 1 2 13

6 7 14 9 6 3 8 13 9 4 14 10 9 15 9

2 7 14 10 10 1 13 9 6 1 3 9 7 5 4

5 14 8 9 13 15 6 11 15 4 2 2 10 14 8

5 2 4 5 2 8 9 6 12 9 5 4 9 14 13

1 6 11 3 9 12 11 1 14 2 10 6 4 12 4

3 3 11 11 9 7 4 3 9 13 6 2 9 14 11

13 4 7 1 8 8 10 8 11 14 14 12 13 1 13

10 11 3 13 7 7 1 1 6 6 1 7 1 15 8

13 5 12 7 15 14 8 9 4 8 15 1 2 2 7

5 4 14 13 3 14 9 5 2 1 11 11 12 5 15

14 3 3 15 9 10 1 11 3 5 10 14 1 8 10

4 4 15 7 10 5 14 14 15 8 3 3 3 15 13

15 13 1 1 1 5 13 1 1 4 1 13 5 9 7

7 6 7 12 10 4 12 6 14 11 9 4 14 5 5

4 10 1 10 13 11 12 7 8 14 1 1 10 2 6

13 15 4 8 6 12 6 2 13 9 11 8 1 3 11

6 7 11 9 7 13 3 2 7 4 4 15 5 5 3

8 10 11 5 2 13 6 2 6 14 4 12 3 7 8

12 15 4 12 9 4 10 14 12 1 15 7 5 6 2

13 6 5 6 14 13 14 15 6 10 3 11 1 7 3

6 10 2 14 4 10 2 6 9 15 12 8 13 10 15

2 5 1 6 2 4 12 5 14 8 1 7 12 7 10

4 14 12 12 3 6 1 9 13 15 5 15 11 1 7

12 5 5 13 11 7 12 12 4 5 15 9 13 1 11

Page 23: Metodos Numericos - Factorizacion Ecuaciones -Apk

15 5 8 1 11 8 7 12 7 8 5 12 12 6 8

9 14 15 7 10 9 1 13 13 14 2 11 2 15 10

15 8 11 15 8 6 13 12 3 4 10 3 6 9 12

9 4 8 7 5 5 3 1 12 13 10 11 1 14 10

15 1 10 5 10 11 2 14 14 3 14 6 1 5 8

12 3 10 10 9 15 5 1 8 7 14 2 1 5 8

3 5 4 13 10 9 5 1 9 14 1 10 3 14 2

8 15 13 12 2 9 10 11 13 11 12 8 3 12 14

10 12 8 9 11 12 11 9 15 8 13 1 8 6 7

14 11 7 12 11 6 15 8 12 10 8 8 7 14 7

10 13 11 12 14 7 15 8 6 2 2 5 9 7 1

15 7 9 7 13 8 12 1 8 4 2 13 5 7 8

2 11 4 13 3 14 5 4 4 1 4 1 9 7 15

5 8 2 8 15 7 15 2 8 13 12 4 9 7 5

8 13 9 15 3 10 7 15 2 1 7 14 2 11 12

2 7 11 12 4 7 4 2 1 9 13 4 2 2 2

4 13 9 2 1 9 10 1 10 2 3 5 1 12 12

3 1 9 4 5 1 1 10 10 9 11 6 3 2 12

11 15 8 2 5 13 1 6 2 10 3 13 8 8 9

5 5 5 9 9 11 3 2 10 12 13 9 13 4 3

12 1 7 1 6 4 4 10 9 5 9 13 5 9 14

9 3 12 8 3 1 11 12 13 14 15 2 3 4 4

4 8 15 15 6 12 7 13 10 12 2 3 1 15 1

11 14 4 11 3 9 13 5 5 2 15 10 15 1 10

1 5 12 14 13 10 6 7 2 5 6 1 4 3 10

9 12 3 8 3 10 13 7 1 14 2 12 10 10 8

15 3 1 5 11 12 12 10 10 2 15 10 4 5 9

6 11 7 3 12 14 9 12 11 12 10 12 4 3 11

9 4 9 15 1 10 3 15 5 2 7 3 12 3 7

Page 24: Metodos Numericos - Factorizacion Ecuaciones -Apk

14 2 4 12 3 2 8 2 7 12 9 12 3 15 9

4 13 3 15 1 11 7 4 6 10 6 12 13 5 7

13 11 11 11 13 7 6 6 2 12 4 14 2 4 2

3 15 6 3 1 10 2 15 2 14 1 7 15 10 6

14 15 8 5 10 10 4 6 2 3 3 3 10 1 9

5 9 11 1 7 11 6 14 11 1 6 5 5 2 2

13 14 9 1 13 1 6 4 4 13 14 5 14 5 2

13 8 8 5 6 4 3 4 4 8 7 7 1 4 5

3 14 12 3 1 3 5 15 1 2 10 6 12 11 11

15 1 11 11 4 14 5 15 11 2 6 10 14 11 7

4 2 5 14 11 8 13 10 9 2 13 15 10 13 8

12 12 13 6 9 11 6 8 9 3 12 5 11 9 1

13 6 10 2 14 11 14 6 12 15 2 4 7 9 2

8 6 9 12 12 2 5 12 13 5 2 14 12 8 6

14 10 1 8 2 4 12 12 6 9 10 14 1 13 6

2 1 13 11 15 5 10 1 3 13 6 5 3 7 15

3 6 2 11 12 14 1 1 3 4 2 2 2 6 12

13 1 13 7 1 4 11 5 11 11 10 12 3 9 10

Columns 91 through 100

14 10 2 11 7 3 13 3 10 15

8 3 3 11 5 8 4 12 2 10

6 2 10 5 5 1 7 7 2 4

14 14 11 9 9 5 6 10 2 14

4 9 14 6 11 5 11 6 12 6

3 7 10 12 13 15 15 7 9 1

10 2 13 2 4 4 4 11 13 4

4 9 11 15 8 8 12 15 2 14

Page 25: Metodos Numericos - Factorizacion Ecuaciones -Apk

3 2 12 12 7 7 8 14 4 14

5 4 9 1 4 13 12 10 1 9

5 3 1 14 12 1 14 15 10 9

1 5 3 13 12 12 4 10 5 1

4 6 7 11 6 9 15 12 11 2

11 14 9 14 5 1 1 14 2 4

15 14 6 7 8 8 9 4 8 13

4 12 10 6 5 7 14 2 1 6

10 2 9 2 3 8 3 13 2 5

15 7 12 15 6 10 7 7 8 4

8 6 3 14 5 8 5 11 11 5

5 7 8 1 4 12 9 15 10 7

9 15 6 11 10 15 13 5 4 3

9 4 15 10 15 12 6 5 10 9

2 2 15 7 3 7 10 9 11 10

9 13 14 8 14 2 15 9 5 11

3 1 7 6 9 15 13 10 13 6

4 15 12 7 3 6 13 9 3 15

8 13 14 1 11 12 15 3 4 4

13 15 6 7 10 13 3 7 9 12

11 12 2 2 5 13 11 6 14 6

8 10 8 1 8 9 12 2 13 13

14 15 6 9 1 5 13 4 9 6

15 9 13 10 1 12 11 15 1 11

7 8 3 12 12 8 5 14 15 6

5 4 4 4 2 8 1 12 12 14

14 3 8 11 11 8 2 3 6 12

8 8 2 11 12 7 5 9 14 7

14 11 4 8 12 3 13 1 11 7

Page 26: Metodos Numericos - Factorizacion Ecuaciones -Apk

4 15 10 14 11 5 14 11 4 6

2 6 2 12 15 14 7 13 3 7

2 4 10 8 5 14 15 14 13 6

9 6 14 12 15 8 1 3 5 2

7 2 8 11 9 10 13 5 5 7

6 10 5 15 10 11 8 12 7 10

12 6 12 2 15 3 15 8 12 5

7 14 15 14 4 9 14 9 3 7

11 7 10 9 15 3 3 14 11 2

14 14 8 2 3 1 6 15 10 8

13 4 7 15 15 1 1 1 13 5

1 12 3 13 15 15 7 6 6 1

15 13 7 1 3 8 7 9 2 14

14 7 8 5 1 3 5 12 13 4

10 9 13 7 5 10 14 15 11 11

1 2 11 10 9 9 8 11 9 3

15 4 10 14 12 5 11 5 12 15

6 9 2 7 10 11 10 15 12 8

6 8 2 11 5 6 13 14 9 14

8 14 9 15 7 4 4 7 13 11

9 10 7 7 13 4 12 11 11 8

15 8 9 10 10 6 7 9 9 10

13 10 1 14 5 1 1 15 11 6

8 2 9 14 8 6 14 6 15 8

14 1 10 3 14 9 15 14 10 12

6 12 8 4 3 9 2 14 13 5

1 5 3 10 13 2 8 6 3 5

5 1 12 12 3 9 12 11 12 6

5 14 12 4 2 8 2 14 4 14

Page 27: Metodos Numericos - Factorizacion Ecuaciones -Apk

7 1 5 6 1 10 1 14 7 2

8 2 8 6 1 12 7 2 12 4

11 9 4 7 15 3 2 1 6 5

6 7 3 3 14 15 15 9 1 6

15 1 13 12 1 9 15 1 4 11

5 1 2 2 11 14 14 3 1 14

12 4 3 14 15 10 15 1 10 1

14 2 15 2 4 3 11 12 4 2

9 10 9 12 2 1 11 3 7 1

14 8 9 13 6 1 6 15 3 3

1 2 15 7 11 3 1 12 14 1

9 7 2 10 10 8 7 13 6 8

1 14 14 6 7 3 9 7 4 4

3 9 14 12 14 2 9 5 12 14

7 11 4 9 1 9 12 11 1 11

4 15 3 10 8 15 10 13 1 8

9 9 10 13 3 3 15 14 8 2

5 8 3 7 8 3 10 14 15 8

11 8 2 14 9 3 14 13 10 10

9 10 6 8 10 2 2 8 10 10

4 12 7 10 4 11 13 8 10 7

1 10 2 9 6 7 15 1 14 2

1 11 11 11 5 8 4 7 4 13

3 7 9 9 10 10 14 9 14 4

8 10 15 12 9 14 11 2 1 8

10 3 4 7 11 2 11 6 13 13

2 14 14 14 3 5 11 4 1 8

2 4 10 2 10 1 12 9 7 5

5 6 12 15 12 3 8 7 9 13

Page 28: Metodos Numericos - Factorizacion Ecuaciones -Apk

2 5 6 11 6 2 12 7 3 1

7 15 8 9 6 3 8 1 12 11

5 3 2 3 11 12 14 4 4 14

10 2 14 13 4 14 2 4 3 7

4 11 7 11 15 8 13 11 10 8

LA MATRIZ DE TERMINOS NO HOMOGENEOS (MATRIZ B) ES:

16

97

88

49

41

13

93

1

19

33

6

15

73

49

34

24

46

19

33

27

84

70

Page 29: Metodos Numericos - Factorizacion Ecuaciones -Apk

34

59

29

27

26

68

52

8

6

26

44

29

68

95

78

64

76

75

59

78

40

61

25

30

2

35

15

42

16

Page 30: Metodos Numericos - Factorizacion Ecuaciones -Apk

83

74

10

83

23

11

67

96

82

63

33

28

44

36

88

1

70

34

31

65

93

90

100

8

13

99

10

69

93

Page 31: Metodos Numericos - Factorizacion Ecuaciones -Apk

15

89

2

35

24

99

85

80

91

79

84

33

75

67

29

34

91

4

70

21

LA MATRIZ "L" DEL SISTEMA ES:

Columns 1 through 9

1.0000 0 0 0 0 0 0 0 0

0.0667 1.0000 0 0 0 0 0 0 0

0.2667 -0.0654 1.0000 0 0 0 0 0 0

0.0667 0.2290 0.5513 1.0000 0 0 0 0 0

0.8667 -0.4579 -0.0425 -0.3977 1.0000 0 0 0 0

Page 32: Metodos Numericos - Factorizacion Ecuaciones -Apk

0.1333 0.1075 0.0934 0.0724 0.1131 1.0000 0 0 0

0.8667 -0.3879 -0.1132 0.1992 0.1988 0.5422 1.0000 0 0

0.5333 -0.1308 0.7884 0.6622 -0.0775 0.6525 0.4365 1.0000 0

0.3333 -0.0467 0.5520 -0.2063 0.6721 0.1851 0.3704 -0.3141 1.0000

0.6000 0.2383 -0.0134 0.4013 -0.3967 0.3996 0.8335 0.5385 0.2143

0.6667 -0.3738 0.5541 0.7330 -0.4362 0.2191 0.1612 0.8499 0.1690

0.2000 0.7570 -0.3857 0.3095 0.2736 -0.6298 0.4039 -0.4341 0.6737

1.0000 -0.1402 -0.0856 -0.1735 0.6991 0.1605 0.5717 0.3280 0.0857

0.2000 0.8972 -0.2243 0.6364 -0.1422 0.2401 0.1703 -0.1238 0.2135

0.5333 0.1495 0.5053 0.4783 0.1897 -0.7553 0.3142 -0.2337 0.2424

0.9333 0.3318 -0.8146 0.1029 0.0162 -0.7178 0.8248 -0.4480 0.1174

0.0667 0.9299 -0.6865 0.1287 0.4256 -0.6945 0.0707 -0.4012 0.1070

0.6667 0.4673 -0.3708 0.0279 0.1392 0.2108 -0.1012 -0.2982 -0.5416

0.9333 -0.6495 0.7820 0.0649 0.1738 0.1304 0.0589 0.3592 0.2725

0.2000 0.3364 -0.1883 0.4757 -0.0355 0.3165 0.4350 -0.4152 0.6904

0.1333 0.2477 0.6334 -0.1583 0.4834 0.8332 0.3259 0.2304 0.6779

0.9333 -0.5794 0.0297 -0.3294 0.7013 0.5625 0.3586 -0.2780 -0.1594

1.0000 -0.2804 0.0559 -0.5880 0.9919 -0.8258 0.4419 -0.0770 0.6125

1.0000 -0.4907 0.3439 0.5020 0.0932 0.0504 0.3948 0.3025 0.3316

0.4000 0.1121 -0.2647 0.1650 0.2601 0.8905 0.6224 -0.2891 0.4410

0.6000 0.3785 -0.2307 0.1170 0.2803 -0.0299 0.4836 0.0666 -0.1296

0.4000 0.5327 -0.2350 -0.3202 0.5618 -0.7099 0.3143 -0.9079 0.7893

0.3333 -0.0467 0.5520 0.8846 -0.0664 -0.0331 0.3952 0.4021 0.2051

0.8000 0.2243 -0.7565 -0.6756 0.5242 0.6425 0.2450 -0.3324 0.1472

0.6667 -0.3738 0.2512 -0.1923 0.8818 -0.0673 0.4226 0.0581 0.8706

0.3333 0.3738 -0.2512 -0.1973 0.5999 0.3560 0.1915 -0.1190 -0.0868

0.4667 -0.0794 0.3326 0.3232 0.3520 -0.3517 0.1103 -0.3706 0.6947

0.6000 -0.3224 0.5527 -0.2438 0.6059 -0.0884 0.0421 0.2665 0.5793

0.7333 -0.3551 0.1062 0.0592 0.5769 0.3402 0.0135 0.3774 0.0086

Page 33: Metodos Numericos - Factorizacion Ecuaciones -Apk

0.5333 0.1495 0.2024 0.2542 0.3689 -0.8086 0.0605 0.2029 0.3204

0.5333 -0.2710 0.7028 0.1770 0.5638 0.4146 -0.3319 0.6439 -0.0492

0.9333 -0.1589 0.0594 -0.5808 0.8325 -0.4580 0.3639 -0.2001 0.0276

0.4000 -0.0981 0.8563 -0.1742 0.5883 0.6588 0.1104 0.2539 0.3643

0.0667 0.7897 -0.5449 0.7271 -0.2484 -0.5218 -0.1979 -0.3100 -0.2274

0.8000 -0.1963 0.5768 -0.5457 0.9807 -0.0058 -0.4156 0.2233 -0.1487

0.2667 0.2150 0.3383 0.1399 0.4500 0.7493 -0.2724 0.5304 -0.4894

0.7333 -0.0748 0.4289 0.2455 -0.0847 -0.0705 0.6031 0.1301 0.4220

0.7333 -0.0748 0.2017 -0.2147 0.5479 0.3092 0.4552 -0.2279 0.3581

0.9333 0.0514 0.3015 0.1822 -0.0471 -0.5836 0.5826 0.0684 0.0052

0.8000 -0.0561 -0.4735 0.2875 0.4871 -0.5932 0.4615 0.0754 0.4413

0.4000 0.3224 -0.5527 -0.1458 0.5336 0.0896 0.5595 -0.6011 0.1673

0.7333 0.3458 0.1557 -0.6975 0.4526 0.2569 -0.2028 0.1791 0.0708

0.1333 0.8785 -0.7608 0.6404 -0.3874 0.2241 0.0991 -0.1553 -0.0115

0.8000 -0.4766 0.1783 -0.3400 0.4481 -0.2515 0.4977 -0.4308 0.8078

0.2000 0.5467 0.3567 0.2941 0.1573 0.3867 0.0051 0.0394 -0.2420

1.0000 0.0701 -0.6008 0.1463 0.0113 0.3467 0.7371 0.1865 -0.4935

0.5333 0.1495 0.2781 -0.1378 0.7079 -0.1236 0.0888 0.2117 0.1030

0.8000 -0.1262 -0.4027 -0.3093 0.5469 -0.3800 0.2774 -0.5961 -0.0058

0.6667 -0.2336 0.0340 0.3026 0.1922 -0.3637 0.7093 -0.2311 0.3411

0.8000 -0.1963 0.3496 0.2408 0.0199 0.5007 0.5978 0.3690 -0.1439

0.6667 0.1869 0.1394 -0.1851 0.3776 0.4902 0.5439 -0.0285 -0.1577

0.1333 0.4579 0.0425 0.5535 -0.2013 0.1237 0.0253 0.2117 0.3896

0.8000 -0.3364 0.2640 0.6127 -0.0780 -0.1310 0.1613 0.4964 0.1267

0.0667 0.8598 -0.3128 -0.1662 0.0214 -0.1938 -0.2554 -0.5990 -0.1415

0.8667 -0.5981 0.4777 0.5003 -0.1404 0.0545 0.2623 0.8223 -0.2656

0.2000 0.8972 -0.7544 0.1858 -0.0711 0.4015 0.4548 -0.0394 -0.1686

0.8000 0.0841 0.2937 -0.2621 0.1657 0.6014 0.2854 0.1828 -0.3241

0.5333 0.5701 -0.6766 0.1098 0.4125 0.0788 0.2516 -0.6003 0.6128

Page 34: Metodos Numericos - Factorizacion Ecuaciones -Apk

0.4000 0.5327 0.1437 0.1352 0.2099 0.3148 -0.2546 0.4912 0.1827

0.3333 0.0234 0.7841 0.6925 -0.0229 0.7632 0.4133 0.5004 0.0472

0.2667 -0.1355 0.7679 0.8154 0.1862 -0.3686 -0.2795 0.3176 -0.0758

0.6000 -0.0421 0.0425 0.6704 -0.0869 -0.2572 0.3825 0.1406 0.0354

0.2667 0.5654 -0.3185 -0.1387 0.3792 -0.3976 -0.2754 -0.6182 0.3842

0.5333 0.0794 -0.2569 0.2198 0.3314 0.7316 0.5763 0.2291 -0.1250

1.0000 -0.2804 0.1316 -0.0450 0.5919 0.1218 0.1106 -0.0244 0.4253

0.6000 0.0981 0.5824 -0.0278 0.6243 -0.6873 -0.1727 0.2666 0.3182

0.6000 0.5888 -0.5945 -0.1914 0.0427 0.5883 0.5021 0.3320 0.1294

0.8667 0.2430 -0.2958 -0.5993 0.4296 -0.2608 -0.0275 0.1747 -0.1894

0.8000 -0.4766 0.4055 0.1203 0.3857 0.7115 0.5042 0.5868 0.0488

0.1333 0.2477 -0.1238 -0.1340 0.3912 0.3767 0.1138 0.0426 0.5894

0.4667 0.2710 -0.3241 0.0446 0.2812 -0.3030 0.2835 -0.2549 0.2238

1.0000 -0.3505 0.4296 -0.4933 0.6456 -0.2666 0.3791 0.1977 0.5784

1.0000 0.0701 -0.1465 -0.6474 0.6234 0.1293 0.5928 0.2874 0.1777

0.8667 -0.4579 0.5633 -0.4950 0.8112 0.1892 0.4825 0.0204 0.6995

0.4000 0.6729 -0.5280 -0.4462 0.7282 -0.2010 0.0869 -0.1725 0.1149

0.4000 0.3925 -0.3963 0.5996 -0.3878 -0.2982 0.5351 0.2598 0.4475

0.9333 0.1215 -0.3751 0.0193 -0.0345 0.1338 0.5799 -0.0961 -0.4116

0.2000 0.4766 -0.4055 -0.1203 0.1275 0.1681 0.3030 -0.2441 -0.0311

0.2667 -0.1355 0.8436 0.3454 0.0118 0.6735 -0.1215 0.2680 0.3109

0.2667 0.2150 0.6412 0.3639 0.2138 -0.0589 -0.0827 0.4734 0.1576

0.1333 0.5981 0.4310 -0.2177 0.5141 -0.5499 0.0347 -0.0553 0.6902

0.3333 0.2336 0.6476 -0.0127 0.6443 0.3061 -0.4514 0.1889 -0.3144

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Page 78: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 86: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 87: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 88: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 89: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 90: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 91: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 92: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 93: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 94: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 95: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 96: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 97: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 98: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 100: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 101: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 102: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 103: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 104: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 105: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 106: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 107: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 108: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 109: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 110: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 111: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 112: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 113: Metodos Numericos - Factorizacion Ecuaciones -Apk

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Page 114: Metodos Numericos - Factorizacion Ecuaciones -Apk

-16.1014

-6.9127

-8.9040

1.4580

-14.2215

5.5461

0.0568

-7.9980

-8.8759

-11.1228

5.8067

-1.5079

13.6264

-7.5086

-0.0150

-17.9247

-3.9174

7.3279

6.7488

15.8261

3.6306

8.3005

-4.4702

18.9565

-7.3444

4.5465

-0.2635

1.0089

8.0115

Page 115: Metodos Numericos - Factorizacion Ecuaciones -Apk

6.3975

-12.0975

-31.3538

2.9804

-6.0397

-12.5678

-6.1876

-12.3104

6.1695

-9.7649

8.0022

4.3232

6.6474

-9.4209

1.6474

3.9374

-2.1052

-5.1147

6.3219

18.2701

9.1340

9.6846

12.4850

-7.7449

4.7605

6.9764

10.5701

13.7556

0.3441

Page 116: Metodos Numericos - Factorizacion Ecuaciones -Apk

-9.3001

-15.7159

-2.2653

-16.7579

-7.1249

15.8163

-1.7435

3.2681

-2.9314

6.2793

-1.5650

-10.1607

22.8350

31.7880

-19.6969

-40.3446

-8.1744

2.4965

-29.0152

9.3309

-2.4069

-32.7441

-9.3077

29.4950

14.1944

37.0999

-15.7827

0.2674

-15.2679

Page 117: Metodos Numericos - Factorizacion Ecuaciones -Apk

LA MATRIZ "Y" DEL SISTEMA ES:

16.0000

95.9333

90.0093

-23.6557

65.4797

-13.5489

125.5712

-91.1777

-153.0632

19.8664

108.3962

-33.0515

-1.4694

28.7725

-39.7092

-84.5017

17.1481

-159.0803

33.2331

24.4563

-22.7056

27.5735

-66.3066

31.2079

-28.4651

47.0842

-4.7066

Page 118: Metodos Numericos - Factorizacion Ecuaciones -Apk

30.6732

9.9152

-107.4867

-11.0864

-64.5866

92.1633

98.0154

41.8410

-48.6950

114.4918

21.4266

60.8378

-13.2970

-96.3790

87.0907

10.7039

-63.2312

-227.2539

84.2511

-155.4646

0.5768

-41.0686

-3.3888

-34.5813

94.6988

39.8562

-130.2034

-52.7959

49.0687

Page 119: Metodos Numericos - Factorizacion Ecuaciones -Apk

32.3198

-37.6717

-3.0054

116.6401

16.1684

41.2782

0.1150

63.9859

7.0170

19.8491

-45.1652

134.8747

-187.8338

-60.2809

180.6529

119.2889

-29.5361

-6.7595

-178.6210

-53.8135

-67.3145

-2.0070

-22.3459

-140.2138

-210.9267

-252.3177

-351.4135

-141.5974

-70.3706

Page 120: Metodos Numericos - Factorizacion Ecuaciones -Apk

212.7952

-173.6856

177.8737

295.7215

36.7096

192.3807

148.6715

89.0308

353.8057

26.2074

344.6458

-38.0852

13.6580

-73.3659

120.5394

LA SOLUCIÓN DEL SISTEMA (X) es:

2.9025

-7.4942

-18.0983

-0.0565

-0.1366

-3.3054

8.9587

-7.3442

-15.4207

-1.9048

-0.8529

16.8473

Page 121: Metodos Numericos - Factorizacion Ecuaciones -Apk

7.9585

24.5668

-3.4465

1.3256

1.2929

17.0528

9.0756

12.3572

-2.6899

-7.5866

3.8293

-1.6406

-6.0387

9.5031

-8.7278

20.4567

4.2943

-0.9118

-9.8352

12.0585

-35.8035

17.5162

10.5005

3.8020

-8.3191

8.7514

-11.2186

-8.4958

-7.4837

Page 122: Metodos Numericos - Factorizacion Ecuaciones -Apk

-17.3318

-18.7125

11.3152

-3.1257

21.1805

4.8183

4.8372

-8.7050

-1.4261

11.4464

7.3585

-11.4244

7.4648

-19.8216

-3.7176

-0.7606

-11.9383

-6.0409

-15.2470

-2.0571

-16.2461

-5.2763

6.6042

-17.5584

1.3186

0.1193

15.7387

22.4110

25.4203

Page 123: Metodos Numericos - Factorizacion Ecuaciones -Apk

-2.0513

1.1967

-12.9607

3.8657

11.0801

-23.1913

12.4286

-8.3262

-23.0980

-8.0260

-9.3470

9.2913

0.6916

-4.4231

10.8087

15.3172

-2.8365

13.4608

8.9700

4.6095

-3.0984

-5.3575

-8.9691

2.2678

-11.8266

4.6992

10.9217

4.9888

6.9782

Page 124: Metodos Numericos - Factorizacion Ecuaciones -Apk

-7.8950

>>