%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% MATLAB 341 worksheet
%%% this file helps to get familiar with basic elements of MATLAB
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%% M. Peszynska,  2008/10
%% Copyright Department of Mathematics, Oregon State University
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%%% INSTRUCTIONS: please type every line yourself
%%%               ignore all lines and text beginning with %
%%%		  replace {yourname} etc. by yourname 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
diary yourname
%% elementary arithmetic operations, variables, and functions
3*pi+sqrt(4)
t = pi/4
(cos(t))^2 + (sin(t))^2  
%% input a column vector
x = [1; 2; 3]
%% input a row vector 
y = [1 2 3]
%% change from a row vector to column vector
x = y'
%% operations on vectors: multiply a vector by a scalar
pi * x
y = y'
%% (now y is a column vector)
%% dot (inner) product of two column vectors
x, y, x'*y
%% compute outer product 
x * y'
%% compute a vector as a component-by-component product of x and y
x.*y
%%%%%%%%%%% EXERCISE 1: 
%% set up a column vector 8x1 representing today's date, call it a
%% set up a row vector 1x8 representing your birthday, call it b
%% compute all possible products of a and b
%%%%%%%%%%
%% how to input a matrix
A = [2 3 5; 7 11 13; 17 19, 23]
%% how to access its elements
A(1), A(3)
%% the transpose of a matrix
A'
%% how to access the first column and rows from 1:2
A (1:2,1)
%% how to access the first column and all rows
A (1:3,1)
A (:,1)
%% how to get a matrix with random entries
B = rand (3,5)
%%%%%%%%%% EXERCISE 2: 
%%%  Swap the first and last columns of B
%%%  Hint: you must save one of the columns in a vector
%%%%%%%%%% EXERCISE 3: 
%%%   Compute all possible products of A and B 
%%%%%%%%%%
%% how to get the size of a vector/matrix if forgotten
size(x)
size(A)
size(B)
%% identity matrix
I = eye(4)
%% set up an elementary matrix of type I and verify its effect on A
EI = [ 0 1 0; 1 0 0; 0 0 1]
EI*A
A*EI
%%%%%%%%%% EXERCISE 4:
%%  4a: Set up some elementary matrices of type I,II,III
%%  4b: Test their action upon A
%%  4c: Now show how to turn A into row echelon form using elementary matrices
%%%%%%%%%% 
%% compute transpose of B
B'
%% compute determinant of A
det(a)
%% compute inverse of A
inv(A)
%% solve Ax = b
b = [ 1 ; 2 ; 3]
x = A \ b
y = inv(A)*b
%%%%%%%%%% EXERCISE 5: 
%%  Set up matrix C equal to the one from 4x4 class example
%%  5b: Compute its determinant and inverse (if possible)
%%  5c: With the above (and if possible), compute its adjoint.
%%  5d: Solve a linear system with Cy = b where b is the first column of identity matrix
%%      what should y be equal to (see step 5b) ?
%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%% EXERCISE 6 to be turned in:
%%  Set up matrix D of size 3x3 containing your OSU ID
%%  Do exercises 4c, 5b,c,d using D.
%%%%%%%%%% 
%%  Print your worksheet/diary, include comments using %
%%%%%%%%%%