Suppose T : R 3 → R 2 {\displaystyle T:\mathbb {R} ^{3}\to \mathbb {R} ^{2}} is a linear transformation such that
T ( [ 1 1 1 ] ) = [ 1 1 ] , T ( [ 1 0 − 1 ] ) = [ 2 1 ] . {\displaystyle 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 ( [ 1 3 5 ] ) ? {\displaystyle T\left({\begin{bmatrix}1\\3\\5\end{bmatrix}}\right)?}
A: [ 2 1 ] {\displaystyle \;{\begin{bmatrix}2\\1\end{bmatrix}}\quad } B: [ 7 5 ] {\displaystyle \;{\begin{bmatrix}7\\5\end{bmatrix}}\quad } C: [ − 1 1 ] {\displaystyle \;{\begin{bmatrix}-1\\1\end{bmatrix}}\quad } D: [ 0 0 ] {\displaystyle \;{\begin{bmatrix}0\\0\end{bmatrix}}\quad } E: {\displaystyle \;} It is not possible to determine.
