Help with a linear transformation problem 
This is my matrix $A$:
  $$\begin{bmatrix}
1 & -3 & \hphantom{-}2 & \hphantom{-}5 & \hphantom{-}2 & \hphantom{-}0\\
0 & \hphantom{-}0  & \hphantom{-}1 & -2 & \hphantom{-}1 & \hphantom{-}1\\
0 & \hphantom{-}0  & \hphantom{-}0 & \hphantom{-}1 &  \hphantom{-}0 & \hphantom{-}0\\
0 & \hphantom{-}0  & \hphantom{-}0 & \hphantom{-}0 &  \hphantom{-}0 & \hphantom{-}0
\end{bmatrix}$$
a. Define the linear transformation $Tx = Ax$. Fill in the blanks  $$T: \mathbb{R}^{\Box} \to \mathbb{R}^{\Box}$$
  with the dimensions of the domain and codomain.
b. Is every vector $b$ in the codomain the image of a vector under $T$? Explain why or why not.

Im pretty lost on this homework problem. any help would be cool. 

For (a), do you know how matrix multiplication works? How many entries must the vector $x$ have? How many entries will $Ax$ have?
For (b), what do you know about the last entry of $Ax$ (regardless of $x$)?
