1. The problem involves multiplying a 5x1 column vector by a 1x2 row vector. 2. The column vector is $$\begin{bmatrix}0 \\ 0 \\ 0 \\ 3 \\ 2\end{bmatrix}$$ and the row vector is $$\begin{bmatrix}\cos 0.5 & 0.2\end{bmatrix}$$. 3. The multiplication of a column vector $$\mathbf{A}$$ of size 5x1 by a row vector $$\mathbf{B}$$ of size 1x2 results in a 5x2 matrix $$\mathbf{C}$$ where each element $$c_{ij} = a_i \times b_j$$. 4. Calculate each element: $$\mathbf{C} = \begin{bmatrix}0 \times \cos 0.5 & 0 \times 0.2 \\ 0 \times \cos 0.5 & 0 \times 0.2 \\ 0 \times \cos 0.5 & 0 \times 0.2 \\ 3 \times \cos 0.5 & 3 \times 0.2 \\ 2 \times \cos 0.5 & 2 \times 0.2\end{bmatrix} = \begin{bmatrix}0 & 0 \\ 0 & 0 \\ 0 & 0 \\ 3\cos 0.5 & 0.6 \\ 2\cos 0.5 & 0.4\end{bmatrix}$$ 5. This is the final product matrix. 6. Note: $$\cos 0.5$$ is the cosine of 0.5 radians, approximately 0.8776. Final answer: $$\begin{bmatrix}0 & 0 \\ 0 & 0 \\ 0 & 0 \\ 3\cos 0.5 & 0.6 \\ 2\cos 0.5 & 0.4\end{bmatrix}$$