function simple_program

%
% This is prototype code you can use to write executable Matlab programs.  In
% Matlab if you want to comment out a line, you can use the % sign.
%


% Let's make some data and use commands that are necessary to do linear
% regression

x=[1:10];		% Generate a column vector with entries 1 to 5
y=[3:12];		% Generate a column vector with entries 3 to 8


sum(x)			% Sume the elements
sum(y)			% Sum elements

sum(x.^2)		% Sum the square of the x elements

x.*y			% Do element-by-element multiplication.  Does it match up?
sum(x.*y)		% Find a sum of element-by-element multiplication

dot(x,y)		% Do the dot product
abs(-3)			% The absolute value function.




% Now we are going to make some simple plots.  You can just adapt this code when
% for your assignment.  The first argument in the plot command is your x
% variable, followed by your y variable, and plot options.  The figure(1)
% command preceding it opens a new window with the heading of Figure 1

figure(1); plot(x,y,'x');	% Plots x and y with crosses to denote data points.

x1=x+3;
y1=y-5;			% Making some new data.

% Plotting multiple data series on the same plot is easy.  You have the same
% basic setup: x_var, y_var, options and you just repeat it for as many plots you
% wish to make.

figure(2); plot(x,y,'x',x1,y1,'x');

% Once you have plotted something, use the GUI toolbar to add legends, axis
% names, etc.

% For part of your assignment you will write a for loop that calculates
% the powers of a matrix and then multiply that matrix by a vector.  Adapt this
% code for your homework.


A=[0.86 0.08; -0.12 1.14];
%A=[0 1; -0.12 0.5];		% Define a matrix
x=[200;100];			% Define a vector

n=10;				% Number of iterations.

result=zeros(2,n);	% Assign a matrix that has as many columns as our iterations
					% and rows as the size of x

for i=1:n
	y=A^i*x;		% Find the ith power of A and multiply it by x
	
	result(:,i)=y;	% Assign that result to our matrix.
end

% We wish to plot the first row of result against the second one. The plotting
% command 'x-' adds connects the x's.

figure(3); plot(result(1,:),result(2,:),'x-');