1. **Problem statement:** Complete the matrix equality: $$\begin{bmatrix} 2 & 7 - a & 8 \\ -5 & 20 & 20b \end{bmatrix} = \begin{bmatrix} 2 & -12 & 8 \\ -5 & c + 25 & 100 \end{bmatrix}$$ 2. **Formula and rules:** Two matrices are equal if and only if their corresponding elements are equal. 3. **Step-by-step solution:** - Equate corresponding elements: - From first row, second column: $7 - a = -12$ - From second row, third column: $20b = 100$ - From second row, second column: $20 = c + 25$ - Solve each: 1. $7 - a = -12 \implies -a = -12 - 7 = -19 \implies a = 19$ 2. $20b = 100 \implies b = \frac{100}{20} = 5$ 3. $20 = c + 25 \implies c = 20 - 25 = -5$ **Final answer:** $$a = 19, \quad b = 5, \quad c = -5$$