%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%    this is a little matlab script to introduce you to some of the syntax of matlab
%    and how you do basic vector and matrix vector operations.  Have fun. Marc
%
%    To run this script...first start Matlab then either just cut or paste in the lines
%    or just type the name of the script at the prompt.  
%
%       For more help and a matlab tutorial, type helpdesk at the prompt and go to "
%       "Getting Started" under the MATLAB DOCUMENTATION
%  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all
%
%  defining vectors...A column vector can be written in 2 ways
%

% use the ; (semi-colon) to separate rows

disp([' here is x=[ 1; 2; 3]']); % this just spits out some text

x=[ 1; 2; 3]

%
% or write x as a transposed row vector (using the ' (quote) transpose operator)
%
disp([' here is x=[ 1 2 3]''']);

x=[ 1 2 3]'

%
% note the difference between a row vector and column vector (here we use the 
%  transpose operator ' again
%

x_transpose=x'

%
%  We can calculate the length of a vector x several ways
%

% 
%  1)  use the function norm
%
disp([' this is length_x=norm(x)']);

length_x=norm(x)

%
%  2) use the functions dot and sqrt (square root)
%
disp([' this is length_x=sqrt(dot(x,x))']);

length_x=sqrt(dot(x,x))

%
%  or we can use the transpose definition of the dot product and sqrt
%
disp([' this is length_x=sqrt(x''*x)']);

length_x=sqrt(x'*x)

% they should all be the same

%--------------------------------------------------------------
%  Fun with matrices:

% consider the 3x3 matrix given in class

A=[  2   1   3 ;
     4   3   8 ;
    -2   0   3 ]

%
%  and the column vector
%

x=[ 1 -2 1 ]';


%
% calculate b=A*x
%

      disp([' b=A*x']);

      b=A*x
      
%
% let v=the third column of A
%

disp([ ' the third column of A can be extracted using v=A(:,3)']);
v=A(:,3)