Question 4 (6 marks) Given a matrix M, let (M )j denote the entry in the i row and j* column of M. o 11 Consider the following graph and its adjacency matrix P = (: 0 0) 100 a) By inspecting the graph, how many paths (you should also write down the paths) of length 2 are there i. from vertex 2 to vertex 3? ii, from vertex 1 to vertex 1? iii, from vertex 1 to vertex 2? (1 mark) b) Compute P?. Write down the values of (P*)za, (P7)1, and (P?)12. How do these values compare to the ones from part (a)? (1 mark) C) By inspecting the graph, how many paths (you should also write down the paths) of length 3 are there i. from vertex 1 to vertex 2? ii, from vertex 2 to vertex 2? Compute P*. Write down the values of (P}12, (P")z2. Again, what do you notice? (1 mark) d) Can you explain what is going on? You may just analyse a specific example, such as the number of paths of length 2 from vertex 1 to vertex 1, and relating this value to (Py. (Hint: write down the exact calculation done during matrix multiplication that computes (P*)11. Relate the numbers in this calculation to the paths in the graph.)