Matlab Gaussian Elimination Question

I'm trying to find the difference in the values of C1 between solving the following system of equations using the attached gaussian elimination script, vs using the backslash command for matrices in matlab (i.e. x=A\b).

I'm getting an answer of 7.9936e-15, but the correct answer is supposedly 3.5527e-15.

I would appreciate it if someone else could try this quickly to tell me if I'm doing something wrong, or the answer is wrong.

I've simply calculated the matrix using the attached script, calculated the other matrix from the backslash command and then subtracted them from one another.

Thanks.

Answer 1

[John D'Errico]

No. What you fail to understand is those two results ARE the same. The same at least, to within floating point trash. Adding, subtracting and multiplying numbers in various orders does not yield identically the same results when you work in floating point arithmetic.

Do you believe me?

.3 - .2 - .1
ans =
  -2.7756e-17

-(.1 + .2 - .3)
ans =
  -5.5511e-17

Gosh. Different numbers, on the order of what you got, from what SHOULD be identically the same computation. This is as expected. Floating point arithmetic is NOT mathematics. It only looks like mathematics.

[Callum C]

I think I understand. So is the question proposed by my professor not valid?