Suppose you are given the following simplicial complex The faces of (ABCD) are part of the simplicial complex, but the 3-simplex (ABCD) itself not. a. What are the Chain groups C0(X),C1(X), and C2(X) ? b. What is 2(ABC) ? What is 1(EF) ? c. Write down the matrix for 1. What is the kernel for that matrix? In other words what is Z1 ? (What computational tool did you choose to use?) d. What are the generators of Z1(X) ? Which one of these are elements of B1(X) ? e. Find Hn(X) for all n0