(Solved): Consider the following functions from \( \mathbb{R}^{3} \) to \( \mathbb{R}^{2} \). Select all func ...

Consider the following functions from \( \mathbb{R}^{3} \) to \( \mathbb{R}^{2} \). Select all functions that are linear transformations. 1) \( T\left(\left[\begin{array}{l}x \\ y \\ z\end{array}\right]\right)=\left[\begin{array}{c}x+y-1 \\ 2 x-y\end{array}\right] \) a \( T\left(\left[\begin{array}{l}x \\ y \\ z\end{array}\right]\right)=\left[\begin{array}{c}\cos x \\ y\end{array}\right] \) 3 \( T\left(\left[\begin{array}{l}x \\ y \\ z\end{array}\right]\right)=\left[\begin{array}{l}0 \\ z\end{array}\right] \) 4 \( T\left(\left[\begin{array}{c}x \\ y \\ z\end{array}\right]\right)=\left[\begin{array}{c}x y \\ x z\end{array}\right] \) 5 \( T\left(\left[\begin{array}{l}x \\ y \\ z\end{array}\right]\right)=\left[\begin{array}{l}x \\ y\end{array}\right] \)