% Matlab diary from cs111, Oct 8 2007.
%
% This is what I typed in class.  
%
% Type it into Matlab yourself to
% reproduce the output I showed.

diary on
x = 49 \ 147
x = 147 / 49
A = [10 -7 0 ; -3 2 6 ; 5 -1 5]
b = [7 ; 4 ; 6]
49 \ 147
(1/49) * 147
ans
ans - 3
1/49
format long
1/49
A
b
x = A \ b
A * x - b
B = inv(A)
xx = B * b
x
xx - x
A * xx - b
A \ b
A
b
A(2,3)
A(2,:)
A(2,:) = A(2,:) - (-3/10) * A(1,:)
format short
A
b(2) = b(2) - (-3/10) * b(1)
A(3,:) = A(3,:) - (5/10) * A(1,:)
b(3) = b(3) - (5/10) * b(1)
A \ b
A
A(3,:) = A(3,:) - (-25) * A(2,:)
b(3) = b(3) - (-25) * b(2)
x3 =  b(3) / A(3,3)
x2 = (b(2) - A(2,3) * x3 ) / A(2,2)
x1 = (b(1) - (-7)*x2 - 0*x3 ) / A(1,1)
x = [x1; x2; x3]
A * x - b
U = A
L = [ 1 0 0 ; -3/10 1 0 ; 5/10 -25 1 ]
A = [10 -7 0 ; -3 2 6 ; 5 -1 5]
L * U
A = [4 4 2 ; 2 2 2 ; 1 0 1]
b = [10 ; 6 ; 2 ]
A \ b
det(A)
A(2,:) = A(2,:) - (1/2) * A(1,:)
A(3,:) = A(3,:) - (1/4) * A(1,:)
A= rand(3)
P = eye(3)
P * A
P = [0 1 0 ; 1 0 0 ; 0 0 1]
A
P*A
A
A * P
diary off