1. **Problem statement:** Calculate the matrix expression $3A + 4B$ where $$A = \begin{pmatrix}7 & -2 & 3 & -4 \\ 0 & 2 & 1 & -1 \\ -5 & 3 & 2 & 0\end{pmatrix}, \quad B = \begin{pmatrix}2 & -1 & -3 & 1 \\ 7 & -1 & 0 & 4 \\ 8 & -2 & 1 & 5\end{pmatrix}$$ 2. **Formula and rules:** To compute $3A + 4B$, multiply each element of matrix $A$ by 3 and each element of matrix $B$ by 4, then add the corresponding elements. 3. **Calculate $3A$:** $$3A = 3 \times \begin{pmatrix}7 & -2 & 3 & -4 \\ 0 & 2 & 1 & -1 \\ -5 & 3 & 2 & 0\end{pmatrix} = \begin{pmatrix}21 & -6 & 9 & -12 \\ 0 & 6 & 3 & -3 \\ -15 & 9 & 6 & 0\end{pmatrix}$$ 4. **Calculate $4B$:** $$4B = 4 \times \begin{pmatrix}2 & -1 & -3 & 1 \\ 7 & -1 & 0 & 4 \\ 8 & -2 & 1 & 5\end{pmatrix} = \begin{pmatrix}8 & -4 & -12 & 4 \\ 28 & -4 & 0 & 16 \\ 32 & -8 & 4 & 20\end{pmatrix}$$ 5. **Add $3A$ and $4B$ element-wise:** $$3A + 4B = \begin{pmatrix}21+8 & -6-4 & 9-12 & -12+4 \\ 0+28 & 6-4 & 3+0 & -3+16 \\ -15+32 & 9-8 & 6+4 & 0+20\end{pmatrix} = \begin{pmatrix}29 & -10 & -3 & -8 \\ 28 & 2 & 3 & 13 \\ 17 & 1 & 10 & 20\end{pmatrix}$$ **Final answer:** $$\boxed{\begin{pmatrix}29 & -10 & -3 & -8 \\ 28 & 2 & 3 & 13 \\ 17 & 1 & 10 & 20\end{pmatrix}}$$