in Q2(e), when we calculating b_hat, i am not sure which one does b_hat represent. Is b_hat the b when we plug the x_hat we have in (b) into Ax_hat = b or is it just the b that are given in the question and we just need to transform it into two decimal floating point? Thanks in advance.
I am not sure I understand your question.
You are given a (mathematical) A and a (mathematical) b.
In (b) and (c), you are working on a two-dec floating-point system.
You should be able to find Ahat and bhat.
Then do LU, and f/b/s, all using two-dec floating-point. Find xhat.
In Q2e calculate bhat-Ahat*xhat, but this latter calculation in exact arithmetic. Proceed from there.
So the two-dec float is used in (b) and (c) in the initial representation and in all calculations for LU and f/b/s, but not in the rest of the study.
Sorry i will clarify my question. So for A and b, even before any math operations, we will first convert each element in A and b into two-dec floating-point, is my understanding correct?
Yes. Correct.