Exercise Set 7.1
2.
(a)
Since
with equality
if and only if
for all i, properties (i) and (ii)
in Definition 7.1 hold.
Also,

so property (iii) holds.
Finally,

so property (iv) holds.
4.
(c) 4 (d) 12
6.
(c) 4 (d) 12
10.

Using the Cauchy-Buniakowsky-Schwarz (CBS) inequality gives

Thus,
Exercise Set 7.3
1.
(f)
The kth iterates of the Jacobi method are

The first two iterates are

2.
(f)
The kth iterates of the Gauss-Seidel method are

The first two iterates are

6.
(f)
The kth iterates of the SOR method are:

With
and
the first two iterates are:
