Find the product AB, if possible.
-$$A = \left[ \begin{array} { r r r }
4 & 4 & - 6 \
- 3 & - 9 & 5 \
9 & 9 & - 9
\end{array} \right] , B = \left[ \begin{array} { r r r }
- 4 & - 3 & 4 \
6 & - 4 & - 7 \
5 & - 2 & 1
\end{array} \right]$$
A)
$\left[ \begin{array} { r r r } - 22 & - 16 & - 18 \ - 17 & 35 & 56 \ - 27 & - 45 & - 36 \end{array} \right]$
B)
$\left[ \begin{array} { r r r } - 22 & - 17 & - 27 \ - 16 & 35 & - 45 \ - 18 & 56 & - 36 \end{array} \right]$
C)

$\left[ \begin{array} { r r r } 4 & 4 & - 6 \ - 3 & - 9 & 5 \ 9 & 9 & - 9 \ - 4 & - 3 & 4 \ 6 & - 4 & - 7 \ 5 & - 2 & 1 \end{array} \right]$
D)

$\left[ \begin{array} { r r r } - 16 & - 12 & - 24 \ - 18 & 36 & - 35 \ 45 & - 18 & - 9 \end{array} \right]$

Question

Find the product AB, if possible.
-$$A = \left[ \begin{array} { r r r } 
4 & 4 & - 6 \
- 3 & - 9 & 5 \
9 & 9 & - 9
\end{array} \right] , B = \left[ \begin{array} { r r r } 
- 4 & - 3 & 4 \
6 & - 4 & - 7 \
5 & - 2 & 1
\end{array} \right]$$
A)
$\left[ \begin{array} { r r r } - 22 & - 16 & - 18 \ - 17 & 35 & 56 \ - 27 & - 45 & - 36 \end{array} \right]$
B)
$\left[ \begin{array} { r r r } - 22 & - 17 & - 27 \ - 16 & 35 & - 45 \ - 18 & 56 & - 36 \end{array} \right]$
C)

$\left[ \begin{array} { r r r } 4 & 4 & - 6 \ - 3 & - 9 & 5 \ 9 & 9 & - 9 \ - 4 & - 3 & 4 \ 6 & - 4 & - 7 \ 5 & - 2 & 1 \end{array} \right]$
D)

$\left[ \begin{array} { r r r } - 16 & - 12 & - 24 \ - 18 & 36 & - 35 \ 45 & - 18 & - 9 \end{array} \right]$

Quizplus · Accepted Answer

The product of matrices A and B is calculated by multiplying rows of A by columns of B and summing the results for each position in the resulting matrix. The correct product is given in option A, as it follows the rules of matrix multiplication and matches the dimensions of the matrices A and B.

Find the Product AB, If Possible A) [−22−16−18−173556−27−45−36]\left[ \begin{array} { r r r } - 22 & - 16 & - 18 \\ - 17 & 35 & 56 \\ - 27 & - 45 & - 36 \end{array} \right]​−22−17−27​−1635−45​−1856−36​​

Find the Product AB, If Possible A) $\left[ \begin{array} { r r r } - 22 & - 16 & - 18 \\ - 17 & 35 & 56 \\ - 27 & - 45 & - 36 \end{array} \right]$