Suppose that $\displaystyle F: \mathbb{R}^4 \to \mathbb{R}^2$ is a function satisfying

$\displaystyle F(\boldsymbol{a}) = \begin{pmatrix}3\\-1\end{pmatrix}, F(\boldsymbol{b}) = \begin{pmatrix}3\\0\end{pmatrix}, F(\boldsymbol{u}) = \begin{pmatrix}1\\-3\end{pmatrix}, F(\boldsymbol{v}) = \begin{pmatrix}4\\1\end{pmatrix}$ and $\displaystyle F(\boldsymbol{w}) = \begin{pmatrix}0\\4\end{pmatrix}$

Is F a linear map? Explain.

Im not sure how to do this.