The document discusses MATLAB functions including: 1) Using rref() to row reduce a matrix and find its reduced row echelon form. 2) Defining symbolic matrices and calculating their inverse and determinant. 3) Plotting sine and cosine functions for different x values. 4) Calculating derivatives and integrals of functions using diff() and int(), and plotting functions and their derivatives. 5) Plotting functions in 3D using ezsurf().

1. CLASE DE MATLAB #1
1.
a=[2 5 7 4;-1 2 5 1;4 -1 7 8];
>> resul=rref(a)
resul =
1.0000 0 0 0.9839
0 1.0000 0 -0.3387
0 0 1.0000 0.5323
>> syms a b w
>> dj=[a b;w a]
dj =
[ a, b]
[ w, a]
>> invdj=inv(dj);
>> dj*invdj
ans =

2. [ (b*w)/(b*w - a^2) - a^2/(b*w - a^2), 0]
[ 0, (b*w)/(b*w - a^2) - a^2/(b*w - a^2)]
>> det(dj);
>> dj'
ans =
[ conj(a), conj(w)]
[ conj(b), conj(a)]
clc
clear

3. 2.
>> x=[0:1:10];
>> y=sin(5*x);
>> plot(x,y)
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0 1 2 3 4 5 6 7 8 9 10
>> x=0:0.01:10;
>> y=sin(5*x);
>> plot(x,y)

4. 1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0 1 2 3 4 5 6 7 8 9 10
3.
>> syms x
>> fx=sin(5*x);
>> dfx=diff(fx)
dfx =
5*cos(5*x)

5. >> ifx=int(fx)
ifx =
-cos(5*x)/5
Esta función es indefinida
4.
>> x=0:0.01:5;
>> fx=cos(sin(3*x.^2));
>> plot(x,fx)
1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.55
0.5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

6. >> syms x
>> fx=cos(sin(3*x.^2));
>> dfx=diff(fx);
>> ezplot(fx);
>> hold on
>> ezplot(dfx)
-6 x sin(sin(3 x 2)) cos(3 x 2)
15
10
5
0
-5
-10
-15
-6 -4 -2 0 2 4 6
x

7. >> syms x y
>> fx=cos(sin(3*x.^2));
>> ezsurf(fx)
>> ezsurf(fx)
cos(sin(3 x 2))
1
0.9
0.8
0.7
5
5
0
0
-5 -5
y x