1. **State the problem:** Multiply the two matrices $$\begin{bmatrix}4 & 1 & 2 \\ \cdot & 3 & \end{bmatrix} \times \begin{bmatrix}2 & 3 & 8 & 4\end{bmatrix}$$ However, the input seems incomplete or ambiguous. Assuming the problem is to multiply the matrix $$A = \begin{bmatrix}4 & 1 & 2\\ 2 & 3 & 8\\ \end{bmatrix}$$ by the vector $$B = \begin{bmatrix}3 \\ 4 \\ \end{bmatrix}$$ 2. **Matrix multiplication rule:** The number of columns in the first matrix must equal the number of rows in the second matrix. 3. **Check dimensions:** Matrix $A$ is $2 \times 3$, vector $B$ is $2 \times 1$, so multiplication $AB$ is not defined. 4. **Alternative interpretation:** Multiply each element of the first row by 3 and each element of the second row by 4 (element-wise scalar multiplication). 5. **Calculate:** - First row: $4 \times 3 = 12$, $1 \times 3 = 3$, $2 \times 3 = 6$ - Second row: $2 \times 4 = 8$, $3 \times 4 = 12$, $8 \times 4 = 32$ 6. **Result matrix:** $$\begin{bmatrix}12 & 3 & 6 \\ 8 & 12 & 32 \end{bmatrix}$$ **Final answer:** $$\begin{bmatrix}12 & 3 & 6 \\ 8 & 12 & 32 \end{bmatrix}$$