\begin{enumerate}
\item
% Section 10.1: Problems 5, 6. %8ed
  Section 10.1: Problems 3, 4. %10 ed

\item
As in the scalar case, where knowing the approximate value of
$f'(x_*)$ would help to design a fixed point iteration for
solving the equation $f(x)=0$ by finding a suitable equivalent
form $x=g(x)$ by introducing a free parameter $\alpha$.
Try apply this technique to the following system of equations
$$
\begin{array}{ll}
1 x_1 + 2 x_2 + 0.03*\sin(x_1 + x_2) & = 4 \\
5 x_1 + 6 x_2 + 0.07*\cos(x_1 - x_2) & = 8
\end{array}
$$
and find a convergent fixed point iteration.
If the equivalent form is not obvious to you, to use the
trick as in the scalar case, but take $\alpha$
to be a $2 \times 2$ matrix.

\item
% Section 10.2: Problems 7(a,b), 10. %8ed
Section 10.2: Problems 7(a,b), 14. %10 ed