Obtain equations (2), (3), (n-2), (n-1), (n), and set up the matrix A as in (1) p.7-21
for the general case, with the matrix coefficients for rows 1, 2, 3, (n-2), (n-1), n, filled in,
as obtained from equations (1), (2), (3), (n-2), (n-1), (n).
As shown in p.7-21, the first equation is:
(1) p.7-21
According to p.7-20, the general form of the series is:
(2) p. 7-20
From (2) p.7-20, we can obtain n+1 equations for n+1 unknown coefficients
.
After referring to p.7-22, it can be determined that the matrix to be set up is of the following form:
where the rows signify the coefficients
,
and the columns signify
.
Building the coefficient matrix as shown in p.7-22 of the class notes, we can begin to solve for the coefficients
as follows:
Equation associated with
:
j=0:
(1)
Equation associated with
:
j=1:
(2)
Equation associated with
:
j=2:
(3)
Equation associated with
:
j=n-2:
(n-2)
Equation associated with
:
j=n-1:
(n-1)
Equation associated with
:
j=n:
(n)
Using all of the above equations, (1), (2), (3), (n-2), (n-1), (n), we can then determine the A matrix to be: