# Generator sets and the kernel formation (Ex)

From Manifold Atlas

**Exercise 1:**
Let and be two sets of -module generators for the kernel module . These are related by a sequence of elementaray operations. (See [Wall1999, Chapter 6], and/or [Ranicki2002, Chapter 12])

- What is the effect on the kernel formation of of adjoining or deleting a zero?
- What is the effect of permuting elements?
- and of adding a new element which is a linear of combination of the others?