1. The problem asks to find the product of a 1x2 row vector and a 2x2 matrix. 2. The row vector is given as $\begin{bmatrix} 2 & 1 \end{bmatrix}$. 3. The matrix is given as $\begin{bmatrix} -1 & 3 \\ 6 & 0 \end{bmatrix}$. 4. To multiply a 1x2 vector by a 2x2 matrix, multiply the vector by each column of the matrix and sum the products: $$\begin{bmatrix} 2 & 1 \end{bmatrix} \times \begin{bmatrix} -1 & 3 \\ 6 & 0 \end{bmatrix} = \begin{bmatrix} 2 \times (-1) + 1 \times 6 & 2 \times 3 + 1 \times 0 \end{bmatrix}$$ 5. Calculate each element: - First element: $2 \times (-1) + 1 \times 6 = -2 + 6 = 4$ - Second element: $2 \times 3 + 1 \times 0 = 6 + 0 = 6$ 6. Therefore, the product is: $$\begin{bmatrix} 4 & 6 \end{bmatrix}$$ 7. This is a 1x2 row vector resulting from the multiplication. Final answer: $\begin{bmatrix} 4 & 6 \end{bmatrix}$