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A connected graph is a graph in which there is a path between every pair of vertices. An adjacency matrix is a square matrix that represents a graph where the rows and columns represent the graph vertices, and the matrix entry at (i, j) is 1 if there is an edge between vertex i and vertex j, and 0 otherwise.

Define an adjacency matrix to represent the graph and initialize a list to keep track of the visited nodes. The list will have the same number of elements as the number of vertices in the graph and will be initialized with all "False" values, indicating no nodes have been visited yet.

Choose a graph traversal technique, either depth-first search (DFS) or breadth-first search (BFS), to traverse the graph starting from the first vertex. In this solution, we will use DFS. Define a recursive DFS function that takes the adjacency matrix, the current vertex, and the visited list as input. In the DFS function, mark the current vertex as visited, and for each neighbor vertex, if it is not visited and there is an edge between the current vertex and the neighbor vertex (i.e., the corresponding adjacency matrix entry is 1), call the DFS function recursively for the neighbor vertex.

After traversing the graph, check if all vertices have been marked as visited in the visited list. If all vertices are visited, the graph is connected; otherwise, the graph is not connected. Here's the step-by-step algorithm to determine if a graph is connected using its adjacency matrix: 1. Initialize an adjacency matrix of the graph and a list of visited nodes with "False" values. 2. Define a DFS function that takes the adjacency matrix, current vertex, and visited list as input parameters. 3. In the DFS function, mark the current vertex as visited. 4. For each neighbor vertex in the adjacency matrix, if it is not visited and there is an edge between the current vertex and the neighbor vertex, call the DFS function recursively for the neighbor vertex. 5. Call the DFS function with the first vertex as the starting point. 6. Iterate through the visited list to check if all vertices have been visited. 7. If all vertices are visited, the graph is connected; otherwise, the graph is not connected.