Find the product, AB, if possible.
-$$A = \left[ \begin{array} { r r r }
1 & 3 & - 2 \
2 & 0 & 4
\end{array} \right] , B = \left[ \begin{array} { r r }
3 & 0 \
- 2 & 1 \
0 & 4
\end{array} \right]$$
A) $\left[ \begin{array} { r r } - 3 & - 5 \ 6 & 16 \end{array} \right]$

B) $A B$ is not defined.

C) $\left[ \begin{array} { r r } - 5 & - 3 \ 16 & 6 \end{array} \right]$

D) $\left[ \begin{array} { r r r } 3 & - 6 & 0 \ 0 & 0 & 16 \end{array} \right]$

Question

Find the product, AB, if possible.
-$$A = \left[ \begin{array} { r r r } 
1 & 3 & - 2 \
2 & 0 & 4
\end{array} \right] , B = \left[ \begin{array} { r r } 
3 & 0 \
- 2 & 1 \
0 & 4
\end{array} \right]$$
A) $\left[ \begin{array} { r r } - 3 & - 5 \ 6 & 16 \end{array} \right]$

B) $A B$ is not defined.

C) $\left[ \begin{array} { r r } - 5 & - 3 \ 16 & 6 \end{array} \right]$

D) $\left[ \begin{array} { r r r } 3 & - 6 & 0 \ 0 & 0 & 16 \end{array} \right]$

Quizplus · Accepted Answer

The product AB is defined because the number of columns in A (3) matches the number of rows in B (3). The resulting matrix is calculated by multiplying rows of A by columns of B: $$AB = \left[ \begin{array} { r r } (1*3 + 3*(-2) + (-2)*0) & (1*0 + 3*1 + (-2)*4) \ (2*3 + 0*(-2) + 4*0) & (2*0 + 0*1 + 4*4) \end{array} \right] = \left[ \begin{array} { r r } -3 & -5 \ 6 & 16 \end{array} \right]$$

Find the Product, AB, If Possible A) [−3−5616]\left[ \begin{array} { r r } - 3 & - 5 \\ 6 & 16 \end{array} \right][−36​−516​]

Find the Product, AB, If Possible A) $\left[ \begin{array} { r r } - 3 & - 5 \\ 6 & 16 \end{array} \right]$