Exercise 4.6.3

We have the incidence matrix $A=\left[\begin{array}{ccc}\hfill -1\hfill & \hfill 1\hfill & \hfill 0\hfill \\ \hfill -1\hfill & \hfill 0\hfill & \hfill 1\hfill \\ \hfill 0\hfill & \hfill -1\hfill & \hfill 1\hfill \end{array}\right]$, and the weight matrix $C=\left[\begin{array}{ccc}\hfill c_1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill c_2\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill c_3\hfill & \hfill 0\hfill \end{array}\right]$,

so $K=A^T\mathit{CA}=\left[\begin{array}{ccc}\hfill c_1+c_2\hfill & \hfill -c_1\hfill & \hfill -c_2\hfill \\ \hfill -c_1\hfill & \hfill c_1+c_3\hfill & \hfill -c_3\hfill \\ \hfill -c_2\hfill & \hfill -c_3\hfill & \hfill c_2+c_3\hfill \end{array}\right]$