1. **Problem:** Given matrices $$A=\begin{pmatrix}-2 & 3 & 3 \\ 1 & 0 & -4 \\ -3 & 1 & -1\end{pmatrix}, \quad B=\begin{pmatrix}1 & -3 & 0 \\ -1 & 2 & 2 \\ 6 & -1 & 5\end{pmatrix}$$ Find matrix $$C = 2A + B$$. 2. **Formula:** To find $$C = 2A + B$$, multiply each element of matrix $$A$$ by 2, then add the corresponding elements of matrix $$B$$. 3. **Step-by-step calculation:** - Multiply $$A$$ by 2: $$2A = 2 \times \begin{pmatrix}-2 & 3 & 3 \\ 1 & 0 & -4 \\ -3 & 1 & -1\end{pmatrix} = \begin{pmatrix}-4 & 6 & 6 \\ 2 & 0 & -8 \\ -6 & 2 & -2\end{pmatrix}$$ - Add $$2A$$ and $$B$$ element-wise: $$C = 2A + B = \begin{pmatrix}-4+1 & 6+(-3) & 6+0 \\ 2+(-1) & 0+2 & -8+2 \\ -6+6 & 2+(-1) & -2+5\end{pmatrix} = \begin{pmatrix}-3 & 3 & 6 \\ 1 & 2 & -6 \\ 0 & 1 & 3\end{pmatrix}$$ 4. **Answer:** $$C = \begin{pmatrix}-3 & 3 & 6 \\ 1 & 2 & -6 \\ 0 & 1 & 3\end{pmatrix}$$ This completes the calculation of matrix $$C$$.