Chapter 2.6, Problem 1E

Show that the following matrices are symmetric positive-definite by expressing $x^{T}Ax$ as a sum of squares.

a. $\left[\begin{array}{cc}1& 0\\ 0& 3\end{array}\right]$

b. $\left[\begin{array}{cc}1& 3\\ 3& 10\end{array}\right]$

c. $\left[\begin{array}{ccc}1& 0& 0\\ 0& 2& 0\\ 0& 0& 3\end{array}\right]$