1. The problem asks us to find vectors parallel to the vector $$\begin{pmatrix}-4 \\ 2\end{pmatrix}$$. 2. Two vectors are parallel if one is a scalar multiple of the other. 3. The given vector can be written as $$\mathbf{v} = \begin{pmatrix}-4 \\ 2\end{pmatrix}$$. 4. Check each vector given by descriptions: - Vector a points upward and to the right, so its components are approximately positive-positive. Not parallel. - Vector b points downward and to the left, meaning both components are negative-negative. Let's check scalar multiples: If $$\mathbf{b} = k \mathbf{v} = k \begin{pmatrix}-4 \\ 2\end{pmatrix} = \begin{pmatrix}-4k \\ 2k\end{pmatrix}$$. For both components to be negative, $$-4k<0$$ and $$2k<0$$ implies $$k>0$$ and $$k<0" which is impossible. So b is not parallel. - Vector c points slightly upward and to the right (positive-positive). Not parallel. - Vector d points downward and to the right (positive-negative), which would be $$\begin{pmatrix}x>0 \\ y<0\end{pmatrix}$$. Since $$\mathbf{v}$$ has components $$-4$$ (negative) and $$2$$ (positive), no positive scalar multiple can flip signs here. Not parallel. - Vector e points leftward (negative component on x-axis and zero on y-axis), so components approximately $$\begin{pmatrix}<0 \\ 0\end{pmatrix}$$ which cannot be a multiple of $$\mathbf{v}$$. 5. Conclusion: none of these described vectors exactly match scalar multiples of $$\begin{pmatrix}-4 \\ 2\end{pmatrix}$$, so none are parallel.