The correct answer is first option
[tex]\left[\begin{array}{ccc}-80&90&40\\50&0&120\end{array}\right][/tex]
Further explanation:
The addition of matrices is done by adding respective elements of matrices
Given
[tex]A=\left[\begin{array}{ccc}2&8&-4\\4&-6&0\end{array}\right] \\B=\left[\begin{array}{ccc}-9&5&6\\3&3&12\end{array}\right][/tex]
We have to find 5(A+2B)
First of all we have to find 2B
So,
[tex]2B=2\left[\begin{array}{ccc}-9&5&6\\3&3&12\end{array}\right]\\=\left[\begin{array}{ccc}2(-9)&2(5)&2(6)\\2(3)&2(3)&2(12)\end{array}\right]\\=\left[\begin{array}{ccc}-18&10&12\\6&6&24\end{array}\right][/tex]
Now,
[tex]=\left[\begin{array}{ccc}2&8&-4\\4&-6&0\end{array}\right]+\left[\begin{array}{ccc}-18&10&12\\6&6&24\end{array}\right]\\=\left[\begin{array}{ccc}2-18&8+10&-4+12\\4+6&-6+6&0+24\end{array}\right]\\=\left[\begin{array}{ccc}-16&18&8\\10&0&24\end{array}\right][/tex]
Then
5(A+2B)
[tex]=5\left[\begin{array}{ccc}-16&18&8\\10&0&24\end{array}\right]\\=\left[\begin{array}{ccc}5(-16)&5(18)&5(8)\\5(10)&0&5(24)\end{array}\right]\\=\left[\begin{array}{ccc}-80&90&40\\50&0&120\end{array}\right][/tex]
The correct answer is first option
Keywords: Matrices, Addition of matrices
Learn more about Matrices at:
- brainly.com/question/13034173
- brainly.com/question/13165943
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