Use the handshake theorem to find the number of edges of the graph with the following adjaceny matrix. A(G) = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

(b) Find the adjacency matrix for one of the following directed graphs: (i) V1 e3 e2 V3 02 (ii) V4 C V1 es e6 e4 e2 e3 02

). (a) Given the points (1,2), (2,6), and (4,1). Find the equation of the straight line that best fits these points. (b) Find P, the projection matrix on C(A), where A = (c) Verify that P² = P. 1 1 12 1 4

Part 2. A directed graph G has 5 vertices, numbered 1 through 5. The 5 x 5 matrix A is the adjacency matrix for G. The matrices A² and A³ are given below. 0 1 0 0 0 0 0 10 0 10 0 0 0 10 0 1 0 0 1 1 0 1 10 0 0 0 010 0 0 0 0 10 0 0 1 1 0 1 10 1 0 Use the information given to answer the questions about the graph G. (a) Which vertices can reach vertex 2 by a walk of length 3? (b) Is there a walk of length 4 from vertex 4 to vertex 5 in G? (Hint: A* A² - A² .)