Let $f : \mathbb{R}^{4} \to \mathbb{R}^{4}$ be the linear transformation determined by $f(\vec{x}) = A \vec{x}$ where $$A=\left[\begin{array}{cccc} -1 &-3 &-1 &3\cr 1 &3 &2 &-5\cr -1 &-3 &-1 &3\cr 1 &3 &1 &-3 \end{array}\right]$$

1. Find bases (i.e., minimal spanning sets) for the kernel and image of $f$. vector
   $\mathrm{Kernel}(f) = \mathrm{span} \Big\lbrace$ $\Big\rbrace.$
   $\mathrm{Image}(f) = \mathrm{span} \Big\lbrace$ $\Big\rbrace.$
   
   
2. The dimension of the kernel of $f$ is and the dimension of the image of $f$ is .
   
   
3. The linear transformation $f$ is
   injective
   surjective
   bijective
   none of these