Linear maps — reconstructing $T$ from its values

Let $T:\mathbb{R}^{3}\to\mathbb{R}^{2}$ be a linear map such that

$$T\!\begin{pmatrix}1\\0\\0\end{pmatrix}=\begin{pmatrix}1\\0\end{pmatrix}, \quad T\!\begin{pmatrix}0\\1\\0\end{pmatrix}=\begin{pmatrix}0\\1\end{pmatrix}, \quad T\!\begin{pmatrix}0\\1\\1\end{pmatrix}=\begin{pmatrix}1\\1\end{pmatrix}.$$

Then $T(1,1,1)^{\!\top}=$