1. The problem statement, all variables and given/known data Given a few vectors that span a module space, how do you find a set that is a basis for this spanned space consisting of entirely different vectors to the original spanning vectors? 3. The attempt at a solution I assume you find what kind of space is spanned by the vectors first. Then determine a bases for that space. But how do you determine the space spanned by the vectors? i.e determine the space concretely?