Answer:
Option d
[tex]9A+5B=\left(\begin{array}{ccc}79&-88&87\\120&-99&5\\-17&102&-130\end{array}\right)[/tex]
Step-by-step explanation:
First multiply matrix A by 9.
Then multiply the matrix B by 5.
When multiplying a matrix by a number x you must multiply each element of the matrix by x.
Then we perform operation 9A
[tex]9\left(\begin{array}{ccc}6&-7&8\\10&-6&-5\\-3&8&-10\end{array}\right)=\left(\begin{array}{ccc}54&-63&72\\90&-54&-45\\-27&72&-90\end{array}\right)[/tex]
Now we perform operation 5B
[tex]5\left(\begin{array}{ccc}5&-5&3\\6&-9&10\\2&6&-8\end{array}\right)=\left(\begin{array}{ccc}25&-25&15\\30&-45&50\\10&30&-40\end{array}\right)[/tex]
Now we add the resulting matrices
[tex]\left(\begin{array}{ccc}54&-63&72\\90&-54&-45\\-27&72&-90\end{array}\right)+\left(\begin{array}{ccc}25&-25&15\\30&-45&50\\10&30&-40\end{array}\right)=\left(\begin{array}{ccc}79&-88&87\\120&-99&5\\-17&102&-130\end{array}\right)[/tex]
