How to show a mapping $T$ is Linear Suppose $T$ is a mapping such that $T(1,1 )= (2,1 )$ and $T(1,-1) = (2,-1)$
(each set of numbers is a vector)
Can the mapping $T$ be linear?
Please note that the question is not asking if $T$ is a linear transformation. 
Is there a way to show that $T$ is Linear by plotting vectors and show linearity?
If anyone can help me with this question it will be greatly appreciated.   

If $T$ is linear than it can be represented by a matrix:
$$
T= \begin{bmatrix}
a&b\\c&d
\end{bmatrix}
$$
such that:
$$
\begin{bmatrix}
a&b\\c&d
\end{bmatrix}
\begin{bmatrix}
1\\1
\end{bmatrix}=
\begin{bmatrix}
2\\1
\end{bmatrix}
\qquad \land \qquad
\begin{bmatrix}
a&b\\c&d
\end{bmatrix}
\begin{bmatrix}
1\\-1
\end{bmatrix}=
\begin{bmatrix}
2\\-1
\end{bmatrix}
$$
A simple inspection show that this is possible for:
$$
T= \begin{bmatrix}
2&0\\0&1
\end{bmatrix}
$$
