2. Consider the network below: (a) Write down the adjacency matrix for the given netw0rk using the formula. 1, if nodes 2' and j are connected by an edge A = [as]: at\": = . 01 otherWISe. Index your rows and columns in the order s, a, b, c, d, e, f, t. (b) Without doing any matrix multiplication, write down the top row of A2, and explain your reasoning. (c) Draw a tree, with root 5, indicating the shortest path from s to all the other nodes. Use the BFS method from class. (d) Using the data in your tree, employ the recursive algorithm from class to compute the number of shortest paths from s to t. (e) Without doing any matrix multiplication, state and explain the entry in the row of node 3 and the column of node 15 in A3