1. **State the problem:** Simplify the expression $$7\left(-12 + \frac{2}{7}\right) + 4 \begin{pmatrix} -5 & -1 \\ 2 & -1 \end{pmatrix}$$. 2. **Simplify inside the parentheses:** Calculate $$-12 + \frac{2}{7}$$. Convert $$-12$$ to a fraction with denominator 7: $$-12 = \frac{-84}{7}$$. So, $$-12 + \frac{2}{7} = \frac{-84}{7} + \frac{2}{7} = \frac{-82}{7}$$. 3. **Multiply scalar with scalar:** Multiply 7 by $$\frac{-82}{7}$$: $$7 \times \frac{-82}{7} = -82$$. 4. **Multiply scalar with matrix:** Multiply each element of the matrix by 4: $$4 \times \begin{pmatrix} -5 & -1 \\ 2 & -1 \end{pmatrix} = \begin{pmatrix} 4 \times -5 & 4 \times -1 \\ 4 \times 2 & 4 \times -1 \end{pmatrix} = \begin{pmatrix} -20 & -4 \\ 8 & -4 \end{pmatrix}$$. 5. **Add scalar to matrix:** Add scalar $$-82$$ to each element of the matrix: $$-82 + \begin{pmatrix} -20 & -4 \\ 8 & -4 \end{pmatrix} = \begin{pmatrix} -82 + (-20) & -82 + (-4) \\ -82 + 8 & -82 + (-4) \end{pmatrix} = \begin{pmatrix} -102 & -86 \\ -74 & -86 \end{pmatrix}$$. **Final answer:** $$\boxed{\begin{pmatrix} -102 & -86 \\ -74 & -86 \end{pmatrix}}$$