Find the image of a vector by using the standard matrix (for the linear transformation T) Was wondering if anyone can help out with the following problem:

Use the standard matrix for the linear transformation $T$ to find the image of the vector $\mathbf{v}$, where
  $$T(x,y) = (x+y,x-y, 2x,2y),\qquad \mathbf{v}=(3,-3).$$

I found out the standard matrix for $T$ to be:
$$\begin{bmatrix}1&1\\1&-1\\2&0\\0&2\end{bmatrix}$$
From here I honestly don't know how to find the "image of the vector $\mathbf{v}$". Does anyone have any suggestions?

The matrix you've written down is correct.  If you have a matrix $M$ and a vector $v$, the image of $v$ means $Mv$.
Something is a bit funny with the notation in your question.  Your matrix is 4x2, so it operates on column vectors of height two (equivalently, 2x1 matrices).  But the vector given is a row vector.  Still, it seems clear that what you need to calculate is the product $Mv$ that Theo wrote down in the comment.  Do you know how to do that?
