Calculate the matrix multiplication Ax for the given matrices.

This is obtained by multiplying the elements of the first row of the first matrix by the corresponding elements of the column vector and summing them.

$$c_{1,1} = (6)(4) + (2)(-2) + (4)(1)$$ $$c_{1,1} = 24 - 4 + 4$$ $$c_{1,1} = 24$$

This is obtained by multiplying the elements of the second row of the first matrix by the corresponding elements of the column vector and summing them.

$$c_{2,1} = (-1)(4) + (4)(-2) + (3)(1)$$ $$c_{2,1} = -4 - 8 + 3$$ $$c_{2,1} = -12 + 3$$ $$c_{2,1} = -9$$

This is obtained by multiplying the elements of the third row of the first matrix by the corresponding elements of the column vector and summing them.

$$c_{3,1} = (-2)(4) + (9)(-2) + (3)(1)$$ $$c_{3,1} = -8 - 18 + 3$$ $$c_{3,1} = -26 + 3$$ $$c_{3,1} = -23$$

$$Ax = \begin{bmatrix} c_{1,1} \\ c_{2,1} \\ c_{3,1} \end{bmatrix} = \begin{bmatrix} 24 \\ -9 \\ -23 \end{bmatrix}$$

The final answer is $\begin{bmatrix} 24 \\ -9 \\ -23 \end{bmatrix}$.