Exercise 1.7.20

$S=

$\left[\begin{array}{cc}\hfill 5\hfill & \hfill 4\hfill \\ \hfill 4\hfill & \hfill 5\hfill \end{array}\right]$

= 1$2$

$\left[\begin{array}{cc}\hfill 1\hfill & \hfill 1\hfill \\ \hfill -1\hfill & \hfill 1\hfill \end{array}\right]$$\left[\begin{array}{cc}\hfill 1\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 9\hfill \end{array}\right]$$\left[\begin{array}{cc}\hfill 1\hfill & \hfill -1\hfill \\ \hfill 1\hfill & \hfill 1\hfill \end{array}\right]$

$, so $A=1$2$

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

$

$S=

$\left[\begin{array}{cc}\hfill 10\hfill & \hfill 6\hfill \\ \hfill 6\hfill & \hfill 10\hfill \end{array}\right]$

= 1$2$

$\left[\begin{array}{cc}\hfill 1\hfill & \hfill 1\hfill \\ \hfill -1\hfill & \hfill 1\hfill \end{array}\right]$$\left[\begin{array}{cc}\hfill 4\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 16\hfill \end{array}\right]$$\left[\begin{array}{cc}\hfill 1\hfill & \hfill -1\hfill \\ \hfill 1\hfill & \hfill 1\hfill \end{array}\right]$

$, so $A=1$2$

$\left[\begin{array}{cc}\hfill 1\hfill & \hfill 1\hfill \\ \hfill -1\hfill & \hfill 1\hfill \end{array}\right]$$\left[\begin{array}{cc}\hfill 2\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 4\hfill \end{array}\right]$$\left[\begin{array}{cc}\hfill 1\hfill & \hfill -1\hfill \\ \hfill 1\hfill & \hfill 1\hfill \end{array}\right]$

$