K^3/Two lines/To themselves/Exercise

Let ${}G_{1}\neq G_{2}$ and ${}H_{1}\neq H_{2}$ denote lines in ${}K^{3}$. What is the dimension of the space

${}W={\left\{\varphi \in \operatorname {Hom} _{K}{\left(K^{3},K^{3}\right)}\mid \varphi (G_{1})\subseteq H_{1}{\text{ and }}\varphi (G_{2})\subseteq H_{2}\right\}}\,?$

Create a solution