(Solved): et \( T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2} \) be a linear transformation that maps \( u=\l ...

et \( T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2} \) be a linear transformation that maps \( u=\left[\begin{array}{r}-2 \\ 6\end{array}\right] \) into \( \left[\begin{array}{r}-12 \\ 4\end{array}\right] \) and maps \( \mathbf{v}=\left[\begin{array}{r|r|r}-2 \\ -5\end{array}\right] \) into \( \left[\begin{array}{r}-1 \\ 4\end{array}\right] \). Use the fact that \( T \) is linea find the image of \( 2 u+v \) A. \( \left[\begin{array}{r}-13 \\ 8\end{array}\right] \) B. \( \left[\begin{array}{r}-26 \\ 16\end{array}\right] \) C. \( \left[\begin{array}{r}-25 \\ 12\end{array}\right] \) D. \( \left[\begin{array}{r}-6 \\ 7\end{array}\right] \)