Answer:
Option a
[tex]-4A+6B=\left(\begin{array}{ccc}-22&30&32\\-16&-78&48\\42&24&30\end{array}\right)[/tex]
Step-by-step explanation:
First multiply matrix A by -4.
Then multiply the matrix B by 6.
When multiplying a matrix by a number x you must multiply each element of the matrix by x.
Then we perform operation -4A
[tex]-4\left(\begin{array}{ccc}-2&6&1\\1&9&-6\\-9&9&-9\end{array}\right)=\left(\begin{array}{ccc}8&-24&-4\\-4&-36&24\\36&-36&36\end{array}\right)[/tex]
Now we perform operation 6B
[tex]6\left(\begin{array}{ccc}-5&9&6\\-2&-7&4\\1&10&-1\end{array}\right)=\left(\begin{array}{ccc}-30&54&36\\-12&-42&24\\6&60&-6\end{array}\right)[/tex]
Now we add the resulting matrices
[tex]\left(\begin{array}{ccc}8&-24&-4\\-4&-36&24\\36&-36&36\end{array}\right)+\left(\begin{array}{ccc}-30&54&36\\-12&-42&24\\6&60&-6\end{array}\right)=\left(\begin{array}{ccc}-22&30&32\\-16&-78&48\\42&24&30\end{array}\right)[/tex]
