$T$ 是 ${\mathbb{R}}^2$ 到 ${\mathbb{R}}^2$ 的線性轉換，$T\left(\left[\begin{array}{c}1\\ 2\end{array}\right]\right)=\left[\begin{array}{c}1\\ 3\end{array}\right]$，$T\left(\left[\begin{array}{c}1\\ 1\end{array}\right]\right)=\left[\begin{array}{c}4\\ 1\end{array}\right]$，若 $T\left(\left[\begin{array}{c}x\\ y\end{array}\right]\right)=\left[\begin{array}{c}ax+by\\ cx+dy\end{array}\right]$，下列何者正確？