1. The problem is to subtract the vector $$\begin{bmatrix}1 \\ 0 \\ 2 \\ 1 \\ 1 \\ 2 \\ 2\end{bmatrix}$$ from the vector $$(1010)_6$$ interpreted as a vector with digits as components. 2. First, convert the base-6 number $$(1010)_6$$ to decimal or treat each digit as a component of a vector: $$\begin{bmatrix}1 \\ 0 \\ 1 \\ 0\end{bmatrix}$$. 3. Since the first vector has 7 components and the second has 4, we cannot subtract them directly. We need to clarify the problem or assume the second vector is padded with zeros to match dimensions: $$\begin{bmatrix}1 \\ 0 \\ 1 \\ 0 \\ 0 \\ 0 \\ 0\end{bmatrix}$$. 4. Now subtract component-wise: $$\begin{bmatrix}1-1 \\ 0-0 \\ 2-1 \\ 1-0 \\ 1-0 \\ 2-0 \\ 2-0\end{bmatrix} = \begin{bmatrix}0 \\ 0 \\ 1 \\ 1 \\ 1 \\ 2 \\ 2\end{bmatrix}$$. 5. The result of the subtraction is the vector $$\begin{bmatrix}0 \\ 0 \\ 1 \\ 1 \\ 1 \\ 2 \\ 2\end{bmatrix}$$. This completes the subtraction operation.