Find the 5 by 5 matrix that approximatesreplacing these boundary conditions by and . Check that your times the constant vector , yields zero; is

singular.Analogously, if is a solution of the continuous problem, then so is .

Here's my work:

Follow the pattern until you get to because

Therefore let Forward U be labeled F, the matrix is:

Follow the pattern as before, but going backwards, and since [tex] U_{1}=U_{0}=0, you get to because

Let B= Backwards of U

Factor out U to get

Now because that one was for , do I have to do the exact opposite?

? For the first element, I keep getting -1 - 0 for the 1st element in the 5 by 5 matrix, yet the book gets 1, and I have no idea why...

*I worked on this problem from 3 in the afternoon, til 7 at night, and I still don't have a clue how the author got the answer out of the book. The way my professor showed the class how to solve a similar problem is different from what the book did, and that's the examples I'll use to show what I've done so far. I had 3 professors help me, and they were also confused, which means they were unable to answer the question.