The matrix $$A= \left[\begin{array}{cccc} 1 &-3 &3 &5\cr 0.5 &-1.5 &1.5 &2.5\cr -2 &6 &-6 &-10 \end{array}\right]$$ is a matrix of a linear transformation $T: {\mathbb R}^k \rightarrow {\mathbb R}^n$.

1. Find $k$ and $n$.
   $k=$, $n=$,
   
   
2. Find the dimension of the kernel (or null space) and image (or range).
   $\mbox{dim(Kernel}(T))=$ , $\mbox{dim(Image}(T))=$.
   
   
3. Is $T$ surjective (or onto)? choose surjective not surjective
   
   
4. Is $T$ injective (or one-to-one)? choose injective not injective