Capitulo 3

UNIVERSIDAD DE CUENCA
FACULTAD DE CIENCIAS QUIMICAS
ESCUELA DE INGENIERIA INDUSTRIAL

Alumno: Williams Sumba Ciclo: 5 ciclo
Docente: Ing. Paul Álvarez Fecha: 15/10/2015
Materia: Métodos numéricos

3.1 Calcule: C= A+B, D=A-B, E=AB; donde:
A= B=

>> A=[1,2,3;0,1,4;3,0,2]
A =
12 3
0 1 4
3 0 2

>> B=[4,1,2;3,2,1;0,1,2]
B =
4 1 2
3 2 1
0 1 2

>> C=A+B
C =
5 3 5
3 3 5
3 1 4

>> D=A-B
D =
-3 1 1
-3 -1 3
3 -1 0

>> E=A*B
E =
10 8 10
3 6 9
12 5 10

3.3 Calcule E=AB, donde:
A= B=>> A
A =
1 2 3
0 1 4
3 0 2
>> B=[3;5;1]
B =
3
5
1

>> E=A*B
E =
16
9
11


3.5 Calcule E=B+CD, donde:

B= C= D=

>> B=[3,2,1;0,4,3;0,0,6]
B =
3 2 1
0 4 3
0 0 6

>> C=[1,0,2;-1,1,0;0,3,2]
C =
1 0 2
-1 1 0
0 3 2

>>D=[1,0,0;-2,1,0;5,2,7]
D =
1 0 0
-2 1 0
5 2 7
>> E=B+(C*D)
E =
14 6 15
-3 5 3
4 7 20

3.7 Resuelva los siguientes conjuntos de ecuaciones por eliminación de Gauss Jordan:
a)
=
>> A=[4,1,-1;3,2,-6;1,-5,3]
A =
4 1 -1
3 2 -6
1 -5 3

>> X=[9;-2;1]
X =
9
-2
1

>>a=[A X]
a =
4 1 -1 9
3 2 -6 -2
1 -5 3

>> tempo=a(3,:);a(3,:)=a(1,:);a(1,:)=tempo;
>> a
a =
1 -5 3 1
3 2 -6 -2
4 1 -1 9

>> a(2,:)=a(2,:)-a(1,:)*a(2,1)
a =
1 -5 3 1
0 17 -15 -5
4 1 -1 9

>> a(3,:)=a(3,:)-a(1,:)*a(3,1)
a =
1 -5 3 1
0 17-15 -5
0 21 -13 5
>> a(2,:)=a(2,:)./a(2,2)
a =
1.0000 -5.0000 3.0000 1.0000
0 1.0000 -0.8824 -0.2941
0 21.0000 -13.0000 5.0000

>> a(3,:)=a(3,:)-a(2,:)*a(3,2)
a =
1.0000 -5.0000 3.0000 1.0000
0 1.0000 -0.8824 -0.2941
0 0 5.5294 11.1765
>> a(1,:)=a(1,:)-a(2,:)*a(1,2)
a =
1.00000 -1.4118 -0.4706
0 1.0000 -0.8824 -0.2941
0 0 5.5294 11.1765

>> a(3,:)=a(3,:)./a(3,3)
a =
1.0000 0 -1.4118 -0.4706
0 1.0000 -0.8824 -0.2941
0 0 1.0000 2.0213
>> a(2,:)=a(2,:)-a(3,:)*a(2,3)
a =
1.0000 0 -1.4118 -0.4706
0 1.0000 0 1.4894
0 01.0000 2.0213

>> a(1,:)=a(1,:)-a(3,:)*a(1,3)
a =
1.0000 0 0 2.3830
0 1.0000 0 1.4894
0 0 1.0000 2.0213

>> X(1)=a(1,4);
>> X(2)=a(2,4);
>> X(3)=a(3,4);
>> X
X =
2.3830
1.4894
2.0213

b)
=

>> A=[1,1,0;-1,2,-1;0,-1,1.1]
A =
1 1 0
-1 2 -1
0 -11.1

>> X=[0;1;0]
X =
0
1
0

>> a=[A X]
a =
1 1 0 0
-1 2 -1 1
0 -1 1.1 0

>> a(2,:)=a(2,:)-a(1,:)*a(2,1)
a =
1.0000 1.0000 0 0
0 3.0000 -1.0000 1.0000
0 -1.0000 1.1000 0
>> a(2,:)=a(2,:)./a(2,2)
a =
1.0000 1.0000 0 0
0 1.0000 -0.33330.3333
0 -1.0000 1.1000 0

>> a(3,:)=a(3,:)-a(2,:)*a(3,2)
a =
1.0000 1.0000 0 0
0 1.0000 -0.3333 0.3333
0 0 0.7667 0.3333
>> a(1,:)=a(1,:)-a(2,:)*a(1,2)
a =
1.0000 0 0.3333 -0.3333
0 1.0000 -0.3333 0.3333
0 0 0.7667 0.3333

>> a(3,:)=a(3,:)./a(3,3)
a =...