Exercise 1.1.21

We have $C=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 3\hfill \\ \hfill 1\hfill & \hfill 2\hfill \\ \hfill 0\hfill & \hfill 1\hfill \end{array}\right]$ and $R=\left[\begin{array}{ccc}\hfill 1\hfill & \hfill 3\hfill & \hfill 8\hfill \\ \hfill 1\hfill & \hfill 2\hfill & \hfill 6\hfill \end{array}\right]$, and compute ${(C^{T}C)}^{-1}=\frac{1}{16}\left[\begin{array}{cc}\hfill 13\hfill & \hfill -5\hfill \\ \hfill -5\hfill & \hfill 2\hfill \end{array}\right]$, and ${(R{R}^T)}^{-1}=\frac{1}{9}\left[\begin{array}{cc}\hfill 41\hfill & \hfill -55\hfill \\ \hfill -55\hfill & \hfill 74\hfill \end{array}\right]$.

Also $C^{T}A{R}^T=\left[\begin{array}{cc}\hfill 129\hfill & \hfill 96\hfill \\ \hfill 351\hfill & \hfill 261\hfill \end{array}\right]$.

So we have