I think you mean abasis...

First off, in order for this set to be a basis of , it must have span

This means that

We see that the corresponding augmented matrix is

Getting it into RREF (I leave this for you to do), we see that

Since the system has solutions (primarily and ), we see that spans .

Now, we need to show that these elements are linearly independent.

This can be rewritten as

Thus, an augmented matrix can be constructed:

To test for linear independence, the easiest way is to evaluate

This equals

Thus, they are linearly independent. Since this set spans and are linearly independent, they form abasisfor

Does this make sense?

--Chris