Given
[tex]\begin{gathered} A=\begin{pmatrix}6 & -2 \\ -1 & 3 \\ 8 & 1\end{pmatrix}\text{ and } \\ \\ B=\begin{pmatrix}3&5\\ -4&-1\\ 0&2\end{pmatrix} \\ \\ \end{gathered}[/tex]
Find 3A+5B
Solution
[tex]\begin{gathered} 3\begin{pmatrix}6 & -2 \\ -1 & 3 \\ 8 & 1\end{pmatrix}+5\begin{pmatrix}3 & 5 \\ -4 & -1 \\ 0 & 2\end{pmatrix}=? \\ \\ \\ \\ =\begin{pmatrix}18 & -6 \\ -3 & 9 \\ 24 & 3\end{pmatrix}+\begin{pmatrix}15 & 25 \\ -20 & -5 \\ 0 & 10\end{pmatrix}=\begin{pmatrix}33 & 19 \\ -23 & 4 \\ 24 & 13\end{pmatrix} \end{gathered}[/tex]
The final answer
[tex]\begin{pmatrix}33&19\\ -23&4\\ 24&13\end{pmatrix}[/tex]
