Question

Find 9A+5B (Picture provided)

Answer 1

Answer:

Option d

$9A+5B=\left(\begin{array}{ccc}79&-88&87\\120&-99&5\\-17&102&-130\end{array}\right)$

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

$9\left(\begin{array}{ccc}6&-7&8\\10&-6&-5\\-3&8&-10\end{array}\right)=\left(\begin{array}{ccc}54&-63&72\\90&-54&-45\\-27&72&-90\end{array}\right)$

Now we perform operation 5B

$5\left(\begin{array}{ccc}5&-5&3\\6&-9&10\\2&6&-8\end{array}\right)=\left(\begin{array}{ccc}25&-25&15\\30&-45&50\\10&30&-40\end{array}\right)$

Now we add the resulting matrices

$\left(\begin{array}{ccc}54&-63&72\\90&-54&-45\\-27&72&-90\end{array}\right)+\left(\begin{array}{ccc}25&-25&15\\30&-45&50\\10&30&-40\end{array}\right)=\left(\begin{array}{ccc}79&-88&87\\120&-99&5\\-17&102&-130\end{array}\right)$