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Perform the indicated operations.$\begin{bmatrix}-7&8&11\\12&-5&16\end{bmatrix}-3\begin{bmatrix}-4&4&6\\5&-2&7\end{bmatrix}=$[−7 8 1112 −5 16]−3[−4 4 65 −2 7]=​

Question

Perform the indicated operations.[781112516]3[446527]=\begin{bmatrix}-7&8&11\\12&-5&16\end{bmatrix}-3\begin{bmatrix}-4&4&6\\5&-2&7\end{bmatrix}=[−7 8 1112 −5 16]−3[−4 4 65 −2 7]=​

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Solution

First, we need to multiply the second matrix by 3.

3 * [446527]\begin{bmatrix}-4&4&6\\5&-2&7\end{bmatrix} = [12121815621]\begin{bmatrix}-12&12&18\\15&-6&21\end{bmatrix}

Then, we subtract this result from the first matrix:

[781112516]\begin{bmatrix}-7&8&11\\12&-5&16\end{bmatrix} - [12121815621]\begin{bmatrix}-12&12&18\\15&-6&21\end{bmatrix} = [547315]\begin{bmatrix}5&-4&-7\\-3&1&-5\end{bmatrix}

So, [781112516]3[446527]\begin{bmatrix}-7&8&11\\12&-5&16\end{bmatrix}-3\begin{bmatrix}-4&4&6\\5&-2&7\end{bmatrix} = [547315]\begin{bmatrix}5&-4&-7\\-3&1&-5\end{bmatrix}

This problem has been solved

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