1. The problem involves two matrices divided by 5: $$\frac{\begin{bmatrix}7 & a \\ b & c\end{bmatrix}}{5} \quad \text{and} \quad \frac{\begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}}{5}$$ We are asked to find the values of $a$, $b$, and $c$ in question 43, presumably from a system or context where these matrices relate. 2. Since the problem states "Find $a$, $b$, and $c$ in question 43" but does not provide additional equations or context, we assume the matrices are equal: $$\frac{\begin{bmatrix}7 & a \\ b & c\end{bmatrix}}{5} = \frac{\begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}}{5}$$ 3. Multiply both sides by 5 to clear denominators: $$\begin{bmatrix}7 & a \\ b & c\end{bmatrix} = \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}$$ 4. Equate corresponding entries: - Top-left: $7 = 1$ (contradiction, so likely a misunderstanding or typo) - Top-right: $a = 2$ - Bottom-left: $b = 3$ - Bottom-right: $c = 4$ 5. Since $7 \neq 1$, the problem might have a different context, but based on the given data, the only consistent values for $a$, $b$, and $c$ are: $$a = 2, \quad b = 3, \quad c = 4$$ This completes the solution based on the given information.