1 Five people, \(A , B , C , D\) and \(E\), are to be allocated to five tasks, 1, 2, 3, 4 and 5 . The following bipartite graph shows the tasks that each person is able to undertake.
\includegraphics[max width=\textwidth, alt={}, center]{5ee6bc88-6343-4ee6-8ecd-c13868d77049-02_441_437_699_797}

1. Represent this information in an adjacency matrix.
2. Initially, \(A\) is allocated to task 3, \(B\) to task 2 and \(C\) to task 4.
   1. Demonstrate, by using an alternating-path algorithm from this initial matching, how each person can be allocated to a different task.
   2. Find a different allocation of people to tasks.