I know I'm having numeric precision issues with a matrix mutiplication operation, but I can't reproduce the same result using for loops. Using the two matricies found in the attached mat file, run the following script. No matter which method I used to calculate the resulting matrix, I can't reproduce the same result as the matrix multiply. How is the Matlab matrix multiply computed?

`load matriciesC = A*B; % normal matix multiply A is 54 x 3 and B is 3 x 54, so C is 54 x 54`

Ci1 = zeros(54);Ci2 = zeros(54);Ci3 = zeros(54);for i=1:54 for j=1:54 for k=1:3 Ci1(i,j) = Ci1(i,j)+A(i,k)*B(k,j); end for k=3:-1:1 Ci2(i,j) = Ci2(i,j)+A(i,k)*B(k,j); end Ci3(i,j) = A(i,:)*B(:,j); end enddiff = C - Ci1;fprintf('max error using k=1:3: %d\n', max(diff(:)))diff = C - Ci2;fprintf('max error with k=3:-1:1 %d\n', max(diff(:)))diff = C - Ci3;fprintf('max error with A(i,:)*B(:,j) %d\n', max(diff(:)))eps_max_orig = eps(max(abs(C(:))));eps_min_orig = eps(min(abs(C(:))));fprintf('range of eps is [%d, %d]\n', eps_min_orig, eps_max_orig)

## Best Answer