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
Thus, they are linearly independent. Since this set spans and are linearly independent, they form a basis for
Does this make sense?