We make a change of base with the matrix $S=\left[\begin{matrix}p & q \\ 1 & 1\end{matrix}\right]$ so the vector $x= (8, 3)$ of $\mathbb{R}^{2\times 1}$ becomes $x= (1, 2)$ and the vector $y=(5, 2)$ of $\mathbb{R}^{2\times 1}$ becomes $y=(1, 1)$.
How can I get to know what $z=(-1, 0)$ of $\mathbb{R}^{2\times 1}$ becomes?