## How to check if a subset is a generator of a group [closed]

Hello there!

I have a very noob questions about generators: what algorithm do I have to follow so I can proof a finite subset is a generator?

Here is the background story (I'll tell it all because I suck at maths and I might have understood the whole concept wrongly):

I want to know how to compute the image of a vector space morphism. I'll continue on a concrete example:

f:R^2 -> R^2 f(x,y) = (x-y, 2x + y) is the morphism

to find its image, I observe that f(x,y) can be rewritten as x(1,2) + y(-1,1). If I am correct, that means that Img(f) = <(1,2), (-1,1)> (that's the notation we use for set generators). Now the question is: does the {(1,2), (-1,1)} set generate R^2 or not?

other notes: R = the real numbers' set

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This question is not really appropriate for MO; you should ask, for example, on math.stackexchange.com. – Qiaochu Yuan Jan 3 2011 at 17:25
First, I think this question is more appropriate for math.stackexchange.net because it's an undergraduate level question rather than a research level question. Second, your question is really about spanning sets in vector spaces, this is a much more specific and easy to understand situation than generating general groups. Finally, the algorithm here is just applying Gaussian elimination. – Noah Snyder Jan 3 2011 at 17:26