3.6.1

1. Create a reachability matrix describing the above graph.

3.6.2

3.6.3

Above we have a made-up network consisting of academics who have worked together on projects that was presented in the exercises of Chapter 1. Please conduct the following exercises using data from the above graph.

1. Please turn the above graph into an undirected matrix
2. Is the above matrix an asymmetric, symmetric, or antisymmetric matrix?
3. What are examples of non-adjacent ties in the graph?

3.6.4

Please solve the following matrix multiplication problems, if possible. \[ \begin{equation} \begin{bmatrix} 8 & 9 & 3\\ 3 & 2 & 2\\ \end{bmatrix} \begin{bmatrix} 5 & 4\\ 1 & 2\\ 3 & 2\\ \end{bmatrix} = \end{equation} \]

\[ \begin{equation} \begin{bmatrix} 2 & 1 & 4\\ \end{bmatrix} \begin{bmatrix} 3\\ 3\\ 0\\ \end{bmatrix} = \end{equation} \]

\[ \begin{equation} \begin{bmatrix} 8\\ 2\\ \end{bmatrix} \begin{bmatrix} 8 & 5\\ 7 & 6\\ 9 & 3\\ \end{bmatrix} = \end{equation} \]

\[ \begin{equation} \begin{bmatrix} 2 & 5\\ 3 & 5\\ 2 & 5\\ \end{bmatrix} \begin{bmatrix} 2\\ 3\\ \end{bmatrix} = \end{equation} \]

\[ \begin{equation} \begin{bmatrix} 5 & 9 & 1\\ 4 & 5 & 2\\ \end{bmatrix} \begin{bmatrix} 7 & 4\\ 1 & 2\\ 3 & 6 \end{bmatrix} = \end{equation} \]

\[ \begin{equation} \begin{bmatrix} 4 & 8 & 2\\ \end{bmatrix} \begin{bmatrix} 3\\ 7\\ 5\\ \end{bmatrix} = \end{equation} \]

\[ \begin{equation} \begin{bmatrix} 4\\ 5\\ \end{bmatrix} \begin{bmatrix} 4 & 8\\ 5 & 8\\ 9 & 7 \end{bmatrix} = \end{equation} \]

\[ \begin{equation} \begin{bmatrix} 4 & 8\\ 5 & 8\\ 9 & 7 \end{bmatrix} \begin{bmatrix} 4\\ 5\\ \end{bmatrix} = \end{equation} \]

3.6.5

1. Multiply the adjacency matrix for the above graph by itself. What is the resulting matrix and interpret the results