5. [22 marks] Given a graph: 12 4 2 15 3 2 3 3 3 9 4 a) Represent the given graph by using an adjacency matrix. (4 marks) b) Draw the Depth First Search Tree for this graph, starting at Vertex 3. (6 marks) c) Find the Shortest Path from vertex 2 to all other vertexes of the given adjacency matrix. What is the cost of each shortest path? Show each step in detail. (6 marks) d) Find the Minimal Cost Spanning Tree. Show each step in detail. What is the cost of the Minimal Cost Spanning Tree? (6 marks)