disp('Define a row vecor:')
disp('x = [1 2 3 4 5]')
x = [1 2 3 4 5]
pause;

disp('Define a sequence:')
disp('x = [1:5]');
x = [1:5]
pause;

disp('Referencing vector contents:')
disp('x(2)')
x(2)
pause

disp('end is the last entry of the vector')
disp('x(end)')
x(end)
pause

disp('Taking a subvector (whose indices are defined by a vector)')
disp('x(2:4)')
x(2:4)
pause

disp('Taking the transpose of a vector')
disp('x''')
x'
pause

disp('Create a vector of all ones (create a vector of all 0 with zeros(...))')
disp('x = ones(5,1)')
x = ones(5,1)
pause

disp('Scalar-vector multiplication')
disp('3*x')
3*x
pause

disp('Add the same scalar value to all the entries of a vector')
disp('x+1')
x+1
pause

disp('Inner (scalar) product')
disp('x''*x');
x'*x
pause

disp('Outer product (the result is a rank 1 matrix)')
disp('x*x''');
x*x'
pause;

disp('Define a matrix')
disp('A = [1 2 ; 3 4]')
A = [1 2 ; 3 4]
pause;

disp('Take the transpose of a matrix')
disp("A'")
A'
pause

disp('Reference a matrix entry')
disp('A(1,1)')
A(1,1)
pause;

disp('The first index is the rows index, the second index is the columns index')
disp('A(2,1)')
A(2,1)
pause;

disp('Take a row of A')
disp('A(1,:)')
A(1,:)
pause

disp('Take a column of A')
disp('A(:,2)')
A(:,2)
pause

disp('Change the value of x')
disp('x = ones(2,1)');
x = ones(2,1)
pause

disp('Matrix-vector (left) multiplication')
disp('A*x')
A*x
pause

disp('Matrix-vector right multiplication')
disp('x''*A')
x'*A
pause

disp('Define another matrix')
disp('B = [5 6 ; 7 8]')
B = [5 6 ; 7 8]
pause;

disp('Matrix addition')
disp('A+B')
A+B
pause;

disp('Matrix subtraction')
disp('A-B')
A-B
pause

disp('Matrix multiplication')
disp('A*B')
A*B
pause;

disp('Pointwise multiplication') 
disp('A.*B')
A.*B
pause;

disp('Pointwise division')
disp('A./B');
A./B
pause

disp('Solve a set of linear equations:')
disp('x1+x2 = 2')
disp('x1-x2 = 0')
pause
disp('Using Gauss-Jordan elimination:')
disp('A = [1 1 ; 1 -1]; b = [2;0]; x = A\\b');
A = [1 1 ; 1 -1]; b = [2;0]; x = A\b
pause;

disp('or By taking the inverse of A:')
disp('x = inv(A)*b')
x = inv(A)*b
pause;

disp('create a 3x2 matrix')
disp('A = [1 2 3; 4 5 6]''')
A = [1 2 3; 4 5 6]'
pause

disp('Take a row of A')
disp('A(2,:)')
A(2,:)
pause

disp('Take a column of A')
disp('A(:,1)')
A(:,1)
pause

disp('Matrices are stored columnwise:')
disp('A(:)')
A(:)
pause

disp('Reshaping a matrix:')
disp('reshape(A,2,3)')
reshape(A,2,3)
pause


disp('Vectorized functions:')

disp('t=-pi:0.1:pi;')
t=-pi:0.1:pi;
disp('y = sin(t);')
y = sin(t);
disp('Plot the graph')
disp('plot(t,y)');
plot(t,y);
pause