Contents
EJERCICIO 2
clc
clear all
A=[4,-2,-10;2,10,-12;-4,-6,16]
R=[-10,32,-16]'
x=A\R
z=A*x
A =
4 -2 -10
2 10 -12
-4 -6 16
R =
-10
32
-16
x =
2.0000
4.0000
1.0000
z =
-10
32
-16
EJERCICIO 3
clc
clear all
A=[4,-2,-10;2,10,-12;-4,-6,16];
[L,U] = lu(A)
L1=L'
U1=U'
B=[2;4;1]
X=U1*L1*B
L =
1.0000 0 0
0.5000 1.0000 0
-1.0000 -0.7273 1.0000
U =
4.0000 -2.0000 -10.0000
0 11.0000 -7.0000
0 0 0.9091
L1 =
1.0000 0.5000 -1.0000
0 1.0000 -0.7273
0 0 1.0000
U1 =
4.0000 0 0
-2.0000 11.0000 0
-10.0000 -7.0000 0.9091
B =
2
4
1
X =
12
30
-52
EJERCICIO 4
clc
clear all
AUTOVALORES DE UNA MATRIZ
A=[0,1,-1;-6,-11,6;-6,-11,5]
autovalores=eig(A)
A =
0 1 -1
-6 -11 6
-6 -11 5
autovalores =
-1.0000
-2.0000
-3.0000
AUTOVECTORES DE UNA MATRIZ
[autovect autoval]=eig(A)
autovect =
0.7071 -0.2182 -0.0921
0.0000 -0.4364 -0.5523
0.7071 -0.8729 -0.8285
autoval =
-1.0000 0 0
0 -2.0000 0
0 0 -3.0000
EJERCICIO 5
clc
clear all
k=[1.5-2i,-0.35+1.2i;-0.35+1.2i,0.9-1.6i]
R=[30+40i,20+15i]'
v=k\R
k*v
Ps1=(35.0881 - 8.7249i)*(30-40i)
Ps2=(34.3872 - 5.7110i)*(20-15i)
k =
1.5000 - 2.0000i -0.3500 + 1.2000i
-0.3500 + 1.2000i 0.9000 - 1.6000i
R =
30.0000 -40.0000i
20.0000 -15.0000i
v =
35.0881 - 8.7249i
34.3872 - 5.7110i
ans =
30.0000 -40.0000i
20.0000 -15.0000i
Ps1 =
7.0365e+02 - 1.6653e+03i
Ps2 =
6.0208e+02 - 6.3003e+02i
EJERCICIO 7
clc
clear all
x=[0,0.5,1,1.5,2,2.5,3,3.5,4,4.5,5]';
y=[10,10,16,24,30,38,52,68,82,96,123]';
M=[x.^2,x,ones(size(x))];
p=M\y
figure(1)
hold on
plot(x,y,'ro','markersize',4,'markerfacecolor','r')
z=@(x) polyval(p,x);
fplot(z,[x(1),x(end)])
xlabel('x')
ylabel('y')
grid on
title('Polinomio aproximado a los valores')
hold off
p =
4.0233
2.0107
9.6783
EJERCICIO 8
clc
clear all
figure(2)
wt=0:0.05:3*pi;
v=120*sin(wt);
subplot(2,2,1),plot(v),grid
hold on
i=100*sin(wt-(pi/4));
plot(i),grid
hold off
p=v.*i;
subplot(2,2,2),plot(p),grid
Fm=3.0;
fa=Fm*sin(wt);
subplot(2,2,3),plot(fa),grid
hold on
fb=Fm*sin(wt-2*(pi/3));
plot(fb),grid
fc=Fm*sin(wt-4*(pi/3));
plot(fc),grid
hold off
fR=3.0;
r=fR*cos(wt);
subplot(2,2,4),polar(wt,r),grid
EJERCICIO 13
clc
clear all
figure(3)
k = 5; m = 10; fo = 10; Bo = 2.5; N = 2^m; T = 2^k/fo;
ts = (0:N-1)*T/N; df = (0:N/2-1)/T;
SampledSignal = Bo*sin(2*pi*fo*ts)+Bo/2*sin(2*pi*fo*2*ts);
An = abs(fft(SampledSignal, N))/N;
plot(df, 2*An(1:N/2))
title('funcion numero 1')
figure(4)
k = 5; m = 10; fo = 10; N = 2^m; T = 2^k/fo;
ts = (0:N-1)*T/N; df = (0:N/2-1)/T;
SampledSignal = exp(-2*ts).*sin(2*pi*fo*ts);
An = abs(fft(SampledSignal, N))/N;
plot(df, 2*An(1:N/2))
title('funcion numero 2')
figure(5)
k = 5; m = 10; fo = 10; Bo = 2.5; N = 2^m; T = 2^k/fo;
ts = (0:N-1)*T/N; df = (0:N/2-1)/T;
SampledSignal = sin((2*pi*fo*ts)+(5*sin(2*pi*(fo/10)*ts)));
An = abs(fft(SampledSignal, N))/N;
plot(df, 2*An(1:N/2))
title('funcion numero 3')
figure(6)
k = 5; m = 10; fo = 10; Bo = 2.5; N = 2^m; T = 2^k/fo;
ts = (0:N-1)*T/N; df = (0:N/2-1)/T;
SampledSignal = sin((2*pi*fo*ts)-(5*exp(-2*ts)));
An = abs(fft(SampledSignal, N))/N;
plot(df, 2*An(1:N/2))
title('funcion numero 4')
EJERCICIO 14
clc
clear all
A=imread('WindTunnel.jpg','jpeg');
figure(7)
row=200;
rojo=A(row,:,1);
gr=A(row,:,2);
bl=A(row,:,3);
subplot(2,1,1)
plot(rojo,'r');
title('color rojo de la imagen en función del ancho de la imagen en la fila 200');
subplot(2,1,2)
hist(rojo,0:15:255);
title('Histograma de color rojo en la fila 200');
EJERCICIO 6 (V.2)
clc
clear all
fprintf('Los movimientos a realizar son (1= primera palo, 2= segundo palo, 3= tercer palo: \n');
hanoi(5,1,2,3);
fprintf('\n');
fprintf('Torres de Hanoi resulta con exito');
function [] = hanoi( discos,com,aux,fin )
if discos==1
fprintf('%d->%d',com,fin);
else
hanoi(discos-1,com,fin,aux);
fprintf('\n%d->%d\n',com,fin);
hanoi(discos-1,aux,com,fin);
end
end
Los movimientos a realizar son (1= primera palo, 2= segundo palo, 3= tercer palo:
1->3
1->2
3->2
1->3
2->1
2->3
1->3
1->2
3->2
3->1
2->1
3->2
1->3
1->2
3->2
1->3
2->1
2->3
1->3
2->1
3->2
3->1
2->1
2->3
1->3
1->2
3->2
1->3
2->1
2->3
1->3
Torres de Hanoi resulta con exito