\fConstruct a 4 X 4 matrix, A, with the following property: The 16 entries ofA must include exactly: 6 zeroes, 5 ones, 4 twos 1 three. Your entries may be placed in any position within the matrix. (i) Construct the directed graph, G, whose adjacency matrix is the matrix A. Label your vertices a, b, c, d. (ii) Construct the matrix, A2. (iii) Explain the entries in A2 in terms of paths in your graph G. (iv) Construct the matrix A3. (v) Select any entry in A3 and explain its value in terms of paths in your graph G. (vi) If possible, construct 2 different (directed) paths from vertex a to vertex d. If it is not possible, explain why