1. **State the problem:** We are given the vector $\overrightarrow{AB} = \begin{pmatrix} -10 \\ 2 \end{pmatrix}$ and asked to find $8 \overrightarrow{BA}$ as a column vector. 2. **Recall the relationship between $\overrightarrow{AB}$ and $\overrightarrow{BA}$:** $$\overrightarrow{BA} = -\overrightarrow{AB}$$ This means the vector from B to A is the negative of the vector from A to B. 3. **Calculate $\overrightarrow{BA}$:** $$\overrightarrow{BA} = - \begin{pmatrix} -10 \\ 2 \end{pmatrix} = \begin{pmatrix} 10 \\ -2 \end{pmatrix}$$ 4. **Multiply $\overrightarrow{BA}$ by 8:** $$8 \overrightarrow{BA} = 8 \times \begin{pmatrix} 10 \\ -2 \end{pmatrix} = \begin{pmatrix} 80 \\ -16 \end{pmatrix}$$ 5. **Final answer:** $$8 \overrightarrow{BA} = \begin{pmatrix} 80 \\ -16 \end{pmatrix}$$ This means the vector $8 \overrightarrow{BA}$ has components 80 and -16.