matlab basics : matrix num elements, row/column operations, lu decomposition

%num of matrix elements
numel(A)

%example of row/col operations for complete pivoting

B =

     1     0    -2     1
     2     2     2     0
     2     2     4     0

%swop rows 1 and 3
>> B([1 3],:) = B([3 1],:)


B =

     2     2     4     0
     2     2     2     0
     1     0    -2     1

%swop columns 1 and 3
>> B( :,[1 3]) = B(:,[3 1])

B =

     4     2     2     0
     2     2     2     0
    -2     0     1     1

% it is now z y x 

>> B(2,:) = (-1/2)*B(1,:) + B(2,:)

B =

     4     2     2     0
     0     1     1     0
    -2     0     1     1

>> B(3,:) = (1/2)*B(1,:) + B(3,:) 

B =

     4     2     2     0
     0     1     1     0
     0     1     2     1


>> B([2 3],:) = B([3 2],:)        

B =

     4     2     2     0
     0     1     2     1
     0     1     1     0

>> B( :,[2 3]) = B(:,[3 2])       

B =

     4     2     2     0
     0     2     1     1
     0     1     1     0

%it is now z x y

>> B(3,:) = (-1/2) * B(2,:) + B(3,:)

B =

    4.0000    2.0000    2.0000         0
         0    2.0000    1.0000    1.0000
         0         0    0.5000   -0.5000

>> rref(B)

ans =

     1     0     0     0
     0     1     0     1
     0     0     1    -1

%x = 1
%y = -1
%z = 0



%lu decomposition

[L,U]=lu(some_matrix)