Is there a linear transformation with the given kernel and image? I have this problem : 
$U=\{(x,y,z,t)\in R^4 | y+z+t=0\}$
$W = \{(x,y,z,t) \in R^4 | x+y=0$ and $z=2t\}$
Is there a linear transformation? 
$T : R^4 \rightarrow  R^4$ 
That $\operatorname{Im} T = U$ and $\ker T = W$?
I don't really know where to start, I think it false but I don't have any establishment for this claim.
Any ideas? Thanks.

$$\dim U=3\;,\;\;\dim W=2$$ and by the dimensions theorem:
$$\dim\,\text{Im}\,T +\dim\ker T=4$$
so the answer is no .
