1. **Problem:** Add the two matrices: $$\begin{bmatrix}10 & 2 \\ 3 & 7\end{bmatrix} + \begin{bmatrix}-4 & 6 \\ 2 & 10\end{bmatrix}$$ 2. **Formula:** Matrix addition is done element-wise: $$\text{If } A = \begin{bmatrix}a_{11} & a_{12} \\ a_{21} & a_{22}\end{bmatrix}, B = \begin{bmatrix}b_{11} & b_{12} \\ b_{21} & b_{22}\end{bmatrix}, \text{ then } A + B = \begin{bmatrix}a_{11}+b_{11} & a_{12}+b_{12} \\ a_{21}+b_{21} & a_{22}+b_{22}\end{bmatrix}$$ 3. **Step-by-step addition:** $$\begin{bmatrix}10 + (-4) & 2 + 6 \\ 3 + 2 & 7 + 10\end{bmatrix} = \begin{bmatrix}6 & 8 \\ 5 & 17\end{bmatrix}$$ 4. **Answer:** $$\boxed{\begin{bmatrix}6 & 8 \\ 5 & 17\end{bmatrix}}$$