close all;
clear all;

% This code is a part of a first introduction in Matlab

% test of commands for, while
% -- compute a vector y with n first i^3 terms 
n = 10;
y = [];
for i = 1:n
    y = [y,i^3]
end 

% -- compute and display the smallest nonnegative integer n such that 2^m>= a:
a = 100;
m = 0;
while 2^m < a
    m = m + 1;
end
m 
  
% Define matrix
A = [ 1 2 3; 4 5 6; 7 8 9];

rref(A)

c = [1; 2; 7];
r = [2 4 6];

d = r*A;

d

% find the eigenvalues of A 
D=eig(A);
D
%[V,D]; 

% Define - Plot functions
x = -2.0:.01:2.0; y = exp(-x.^2); 
figure (1); plot(x,y)

x=0:.01:2*pi; y1=sin(x); y2=sin(2*x); y3=sin(4*x); 
figure (2);
plot(x,y1,'--',x,y2,':',x,y3,'+')


x = [0:10]/10;

f1 = sin(x); 
f2 = x.^2;

f3 = ( x.*f1 )./(1 + 3*f2);
figure (3);
plot (x, f3); xlabel('x'); ylabel('f3');

figure(4);
hold on;
g = 1./(1+x.^2);
h = -1./(1+x.^2)
plot (x, g,'r');
plot (x, h,'b');
xlabel('x'); ylabel('f3');
hold off;

figure(5);
g = 1./(1+x.^2);
h = -1./(1+x.^2)
plot(x,g,'r',x,h,'b'); xlabel('x'); ylabel('g,h');