\begin{enumerate}
\item Section 3.5: 
The cubic spline with not-a-knot condition gives rise to a linear system $A x = b$ where
$A$ is an $(n+1)\times (n+1)$ matrix and $x = (c_0, c_1, \cdots, c_n)^T$. 
Eliminating $c_0$ and $c_n$ results in a new equivalent linear system 
$\tilde A \tilde x = \tilde b$ where $\tilde x = (c_1, \cdots, c_{n-1})^T$
and $\tilde A$ can be made symmetric. 
Carry out the details for the case $h_0 = \cdots = h_n = h$ and show that
$\tilde A$ is symmetric and positive definite (hence the original $A$ is non-singular).

\item
% Section 4.1: Problems 7(a), 19, 22, 24, 28, 29. %9th ed
% problem 19 is no good. also it refers to 3.5 problem 17 in 10ed 
%  (problem 15, 9th ed) instead, remove next time.
Section 4.1: Problems         19, 24, 26, 28, 29. %10th ed