Don't use det to try to determine if a matrix is singular.
A = 0.1*eye(400);
det(A)
B = 1e10*[1 1; 1 1+eps];
det(B)
A is a non-zero scalar multiple of the identity matrix and so is not singular, but the determinant underflows to 0.
B is extremely close to singular, but its determinant is close to 20000 because its elements are so large.
Instead of using det to determine if a matrix is singular, use cond to compute the condition number. The closer to 1 the condition number is, the better conditioned the problem is.
cond(A) % 1
cond(B) % around 2e16
