Practica Metodos Num Ricos

1. Calcule C=A+B, D=A-B, E=A*B, donde

A=[1 2 3;0 1 4;3 0 2];
B=[4 1 2;3 2 1;0 1 2];
C=A+B
D=A-B
E=A*B

C =

5 3 5
3 3 5
3 1 4


D =

-3 1 1
-3 -1 3
3 -1 0


E =

10 8 10
3 6 9
12 5 10
2. Calcule B’A’ y (AB) ’, donde Ay B se definen como en el problema anterior. Demuestre que losresultados son idénticos.

A=[1 2 3;0 1 4;3 0 2];
B=[4 1 2;3 2 1;0 1 2];
C=B'*A'
E=(A*B)'

C =

10 3 12
8 6 5
10 9 10


E =

10 3 12
8 6 5
10 9 10
3. Calcule E=AB, donde:

A=[1 2 3;0 1 4;3 0 2];
B=[3;5;1];
E=(A*B)
E =

16
9
11
4. Calcule D=A+E, E=A-E, F=AB, G=BA Y H=BC, donde:


B=[4 1 2;3 2 1;0 1 2;3 10];
C=[7;1;4];
D=A+E
E=A-E
F=A*B
G=B*A
H=B*C
D =

3 5 3 2
0 2 4 3
5 1 7 3


E =

-1 -1 3 0
0 0 4 1
1 -1 -3 3


F =

13 9 10
9 8 9
21 8 10


G =

10 9 20 12
6 8 19 10
6 1 8 8
3 7 13 5


H =

37
279
22

5. Calcule E=B+CD, donde:

B=[3 2 1;0 4 3;0 0 6];
C=[1 0 2;0 4 3;0 0 6];
D=[1 0 0;-2 1 0;5 2 7];
E=B+C*D


E =

14 6 15
7 14 24
30 12 48
6. Resuelva el siguiente conjunto de ecuaciones con MATLAB y verifique los resultados mediante cálculos manuales.


A=[2 1 -3;-1 3 2;3 1 -3];
B=[-1;12;0]
C=A*B
C =

10
37
9






A=[0.1 -0.6 1;-2 80.3;1 6 4];
B=[0;1;2];
C=A*B
C =

1.4000
8.6000
14.0000

7. Resuelva los siguientes conjuntos de ecuaciones por eliminación de Gauss-Jordan:

a=[4 1 -1; 3 2 -6; 1 -5 3]
b=[9; -2; 1]
a=[a, b]
a(1,1:4)=a(1,1:4)/a(1,1)
a(2,1:4)=a(2,1:4)-a(2,1)*a(1,1:4)
a(3,1:4)=a(3,1:4)-a(3,1)*a(1,1:4)
a(2,2:4)=a(2,2:4)/a(2,2)
a(1,2:4)=a(1,2:4)-a(1,2)*a(2,2:4)
a(3,2:4)=a(3,2:4)-a(3,2)*a(2,2:4)a(3,3:4)=a(3,3:4)/a(3,3)
a(1,3:4)=a(1,3:4)-a(1,3)*a(3,3:4)
a(2,3:4)=a(2,3:4)-a(2,3)*a(3,3:4)

a =

4 1 -1
3 2 -6
1 -5 3


b =

9
-2
1


a =

4 1 -1 9
3 2 -6 -2
1 -5 3 1


a =

1.0000 0.2500 -0.2500 2.2500
3.0000 2.0000 -6.0000 -2.0000
1.0000 -5.0000 3.0000 1.0000


a =

1.00000.2500 -0.2500 2.2500
0 1.2500 -5.2500 -8.7500
1.0000 -5.0000 3.0000 1.0000


a =

1.0000 0.2500 -0.2500 2.2500
0 1.2500 -5.2500 -8.7500
0 -5.2500 3.2500 -1.2500


a =

1.0000 0.2500 -0.2500 2.2500
0 1.0000 -4.2000 -7.0000
0 -5.2500 3.2500 -1.2500


a =

1.0000 00.8000 4.0000
0 1.0000 -4.2000 -7.0000
0 -5.2500 3.2500 -1.2500


a =

1.0000 0 0.8000 4.0000
0 1.0000 -4.2000 -7.0000
0 0 -18.8000 -38.0000


a =

1.0000 0 0.8000 4.0000
0 1.0000 -4.2000 -7.0000
0 0 1.0000 2.0213


a =

1.0000 0 02.3830
0 1.0000 -4.2000 -7.0000
0 0 1.0000 2.0213


a =

1.0000 0 0 2.3830
0 1.0000 0 1.4894
0 0 1.0000 2.0213


x =

2.3830
1.4894
2.0213

a=[1 1 0; 2 -1 3; 3 2 -2]
b=[1; 4; -2]
a=[a, b]
a(1,1:4)=a(1,1:4)/a(1,1)
a(2,1:4)=a(2,1:4)-a(2,1)*a(1,1:4)a(3,1:4)=a(3,1:4)-a(3,1)*a(1,1:4)
a(2,2:4)=a(2,2:4)/a(2,2)
a(1,2:4)=a(1,2:4)-a(1,2)*a(2,2:4)
a(3,2:4)=a(3,2:4)-a(3,2)*a(2,2:4)
a(3,3:4)=a(3,3:4)/a(3,3)
a(1,3:4)=a(1,3:4)-a(1,3)*a(3,3:4)
a(2,3:4)=a(2,3:4)-a(2,3)*a(3,3:4)
x=a(1:3,4)

a =

1 1 0
2 -1 3
3 2 -2


b =

1
4
-2


a =

1 1 0 1
2 -1 3 4
3 2 -2 -2


a =

1 1...