Scalar multiplication is done by multiplying each component of the vector by the scalar.
So $3 \mathbf{b} = 3 \begin{pmatrix} 4 \\ 2 \\ -1 \end{pmatrix} = \begin{pmatrix} 12 \\ 6 \\ -3 \end{pmatrix}.$
Vector subtraction is done by subtracting the corresponding components of the vectors.
So $\mathbf{a} - 3 \mathbf{b} = \begin{pmatrix} -7 \\ 0 \\ 1 \end{pmatrix} - \begin{pmatrix} 12 \\ 6 \\ -3 \end{pmatrix} = \begin{pmatrix} -7 - 12 \\ 0 - 6 \\ 1 - (-3) \end{pmatrix} = \begin{pmatrix} -19 \\ -6 \\ 4 \end{pmatrix}.$
Thus, $\mathbf{a} - 3 \mathbf{b} = \boxed{\begin{pmatrix} -19 \\ -6 \\ 4 \end{pmatrix}}.$
The answer is: \begin{pmatrix}-19\-6\4\end{pmatrix}
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Given $\mathbf{a} = \begin{pmatrix} -7 \\ 0 \\ 1 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} 4 \\ 2 \\ -1 \end{pmatrix},$ find $\mathbf{a} - 3 \mathbf{b}.$

### Answer:
