MAESTRIA EN INGENIERIA ESTRUCTURALMATEMATICA APLICADAPRACTICA
GRUPAL DE LABORATORIO N. 3Diego Quiroga MorenoPablo Romano
JaldnOCHABAMBA BOLIVIA
Prctica de MATLAB N. 3Pag. 422 ML1Determine el polinomio
caracterstico de:a)A=[1 2;2 -1];poly(A)ans = 1 0 -5
b)A=[2 4 0;1 2 1;0 4 2];poly(A)ans = 1 -6 4 8
c)A=[1 0 0 0;2 -2 0 0;0 0 2 -1;0 0 -1 2];poly(A)ans = 1 -3 -3 11
-6
Pag. 422 ML2a)A=[1 -3;3 -5];roots(poly(A))ans = -2.0000 +
0.0000i -2.0000 - 0.0000i
b)A=[3 -1 4;-1 0 1;4 1 2];A=[1 -3;3 -5];roots(poly(A))ans
=6.5324 -2.3715 0.8392
c)A=[2 -2 0;1 -1 0;1 -1 0];roots(poly(A))ans = 0 0 1
d)A=[2 4;3 6];roots(poly(A))ans = 0 8
Pag. 422 ML3a)A=[1 2;-1 4];rref(A-3*eye(2))ans = 1 -1 0 0
b)A=[4 0 0;1 3 0;2 1 -1];rref(A+1*eye(3))ans = 1 0 0 0 1 0 0 0
0
c)A=[2 1 2;2 2 -2;3 1 1];rref(A-2*eye(3))ans = 1 0 -1 0 1 2 0 0
0
Pag. 433 ML1a)A=[0 2;-1 3];roots(poly(A))ans = 2
1v1=null(A-2*eye(2));v2=null(A-1*eye(2));P=[v1 v2]P = 0.7071 0.8944
0.7071 0.4472
b)A=[1 -3;3 -5];roots(poly(A))ans = -2.0000 + 0.0000i -2.0000 -
0.0000iNo es diagonizablec)A=[0 0 4;5 3 6;6 0 5];roots(poly(A))ans
= 8.0000 -3.0000
3.0000v1=null(A-8*eye(3));v2=null(A+3*eye(3));v3=null(A-3*eye(3));P=[v1
v2 v3]P = -0.2457 0.7982 0 -0.8355 -0.0665 -1.0000 -0.4915 -0.5987
0
Pag. 433 ML2A=[-1 1 -1;-2 2 -1;-2 2 -1];roots(poly(A))ans = 0
-1.0000
1.0000v1=null(A-0*eye(3));v2=null(A+1*eye(3));v3=null(A-1*eye(3));P=[v1
v2 v3]P = 0.7071 0.5774 0 0.7071 0.5774 0.7071 0.0000 0.5774
0.7071D= inv(P)*A*P; -0.0000 -0.0000 -0.0000 -0.0000 -1.0000
-0.0000 -0.0000 0.0000 1.0000D=[0 0 0;0 -1 0;0 0 1];D^30ans = 0 0 0
0 1 0 0 0 1A30=P*D^30*inv(P)A30 = 1.0000 -1.0000 1.0000 -0.0000
0.0000 1.0000 0 -0.0000 1.0000
Pag. 433 ML3A=[-1 1.5 -1.5;-2 2.5 -1.5;-2 2
-1];roots(poly(A))ans = -1.0000 1.0000
0.5000v1=null(A+1*eye(3));v2=null(A-1*eye(3));v3=null(A-0.5*eye(3));P=[v1
v2 v3]P = 0.5774 0 0.7071 0.5774 -0.7071 0.7071 0.5774 -0.7071
-0.0000D=inv(P)*A*P;D = -1.0000 0 0.0000 -0.0000 1.0000 0.0000
-0.0000 -0.0000 0.5000D=[-1 0 0;0 1 0;0 0 0.5];D30=D^30;D30 =
1.0000 0 0 0 1.0000 0 0 0 0.0000D30 = 1.000000000000000 0 0 0
1.000000000000000 0 0 0 0.000000000931323A30=P*D30*inv(P);
A30 =1.0000 -1.0000 1.0000-0.0000 0.0000 1.0000-0.0000 0.0000
1.0000
A30 =0.999999999999999 -0.999999999068677
0.999999999068676-0.000000000000000 0.000000000931324
0.999999999068676-0.000000000000000 0.000000000000001
0.999999999999999
Pag. 433 ML4
A=[-1 1 -1;-2 2 -1;-2 2 -1];A^2ans = 1 -1 1 0 0 1 0 0 1A^4ans =
1 -1 1 0 0 1 0 0 1A^6ans = 1 -1 1 0 0 1 0 0 1A^16ans = 1 -1 1 0 0 1
0 0 1
A^3ans = -1 1 -1 -2 2 -1 -2 2 -1A^5ans = -1 1 -1 -2 2 -1 -2 2
-1A^7ans = -1 1 -1 -2 2 -1 -2 2 -1
P= 1 1 0 1 1 1 0 1 1
Pag. 444 ML1a)A=[6 6;6 6][V,D]=eig(A)V = -0.7071 0.7071 0.7071
0.7071D = 0 0 0 12
b)A=[1 2 2;2 1 2;2 2 1];[V,D]=eig(A)V = 0.6206 0.5306 0.5774
0.1492 -0.8027 0.5774 -0.7698 0.2722 0.5774D = -1.0000 0 0 0
-1.0000 0 0 0 5.0000
c)A=[4 1 0; 1 4 1;0 1 4];[V,D]=eig(A)V = 0.5000 -0.7071 0.5000
-0.7071 0.0000 0.7071 0.5000 0.7071 0.5000D = 2.5858 0 0 0 4.0000 0
0 0 5.4142
Pag. 444 ML2a)A=[1 2;-1 4];[V,D]=eig(A)V = -0.8944 -0.7071
-0.4472 -0.7071D = 2 0 0 3No es ortogonal,No se puede cambiar por
matriz ortogonal b)A=[2 1 2;2 2 -2;3 1 1];[V,D]=eig(A)V = 0.5482
-0.7071 0.4082 -0.6852 -0.0000 -0.8165 -0.4796 -0.7071 0.4082D =
-1.0000 0 0 0 4.0000 0 0 0 2.0000No es ortogonal,No se puede
cambiar por matriz ortogonalc)A=[1 -3;3 -5];[V,D]=eig(A)V = 0.7071
0.7071 0.7071 0.7071D = -2.0000 0 0 -2.0000No se puede diagonalizar
(no tiene dos vectores propios LI)No se puede cambiar por matriz
ortogonald)A=[1 0 0;0 1 1;0 1 1];[V,D]=eig(A)V = 0 1.0000 0 -0.7071
0 0.7071 0.7071 0 0.7071D = 0 0 0 0 1 0 0 0 2Si es ortogonal, la
matriz A es simtrica1
