Finding a Basis for a Module: Techniques and Examples

[pivoxa15]

Homework Statement

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?

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?

 

[matt grime]

What on Earth does 'concrete' mean? You've been doing this for years in linear algebra - row reduce the vectors until you get something you like. Bear in mind to only do operations invertible in the ring you're dealing with. A concrete example would have really helped, by the way.