The system of linear equations in real $\left ( x,y \right )$ given by $$\left ( x \: y \right )\begin{bmatrix} 2 &5 - 2 \alpha \\ \alpha & 1 \end{bmatrix} = \left ( 0\:0 \right )$$ involves a real parameter $\alpha$ and has infinitely many non-trivial solutions for special value(s) of $\alpha$. Which one or more among the following options is/are non trivial solution(s) of $\left ( x,y \right )$ for such special value(s) of $\alpha$?

1. $x = 2, y = -2$
2. $x = -1, y = 4$
3. $x = 1, y = 1$
4. $x = 4, y = -2$