Science:Math Exam Resources/Courses/MATH221/December 2019/Question 04 (e)/Statement

Suppose $T:\mathbb {R} ^{3}\to \mathbb {R} ^{2}$ is a linear transformation such that

$$T\left({\begin{bmatrix}1\\1\\1\end{bmatrix}}\right)={\begin{bmatrix}1\\1\end{bmatrix}},\quad T\left({\begin{bmatrix}1\\0\\-1\end{bmatrix}}\right)={\begin{bmatrix}2\\1\end{bmatrix}}.$$

What is $T\left({\begin{bmatrix}1\\3\\5\end{bmatrix}}\right)?$

A: $\;{\begin{bmatrix}2\\1\end{bmatrix}}\quad$ B: $\;{\begin{bmatrix}7\\5\end{bmatrix}}\quad$ C: $\;{\begin{bmatrix}-1\\1\end{bmatrix}}\quad$ D: $\;{\begin{bmatrix}0\\0\end{bmatrix}}\quad$ E: $\;$ It is not possible to determine.