Ok, so the question is as follows: Let V and W be linear spaces, each with dimension 2 and each with basis (e1, e2). Let T:V --> W be a linear transformation such that

T(e1 + e2) = 3e1 + 9e2, T(3e1 + 2e2) = 7e1 + 23e2. Compute T(e2 - e1) and determine the nullity and the rank of T.

So my problem is that I don't understand the two T equation that they give you and how they work. Can anyone lead me to the right direction?