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  4. if A =[1 -4 3]and B=[-1&2&1], then (AB)' is equal to

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Q. if $A =\begin{bmatrix}1\\ -4\\ 3\end{bmatrix}$and $B=\begin{bmatrix}-1&2&1\end{bmatrix}$, then $(AB)'$ is equal to

Matrices

Solution:

$\left(AB\right)= \begin{bmatrix}1\\ -4\\ 3\end{bmatrix}\begin{bmatrix}-1&2&1\end{bmatrix}=\begin{bmatrix}-1&2&1\\ 4&-8&-4\\ -3&6&3\end{bmatrix}$
$\left(AB\right)' =\begin{bmatrix}-1&4&-3\\ 2&-8&6\\ 1&-4&3\end{bmatrix}$