Find the product AB, if possible.
-$$A = \left[ \begin{array} { r r r }
1 & 3 & - 2 \
2 & 0 & 5
\end{array} \right] , B = \left[ \begin{array} { r r }
3 & 0 \
- 2 & 1 \
0 & 5
\end{array} \right]$$
A)
$\left[ \begin{array} { r r } - 7 & - 3 \ 25 & 6 \end{array} \right]$
B) $\mathrm { AB }$ is not defined.
C)
$\left[ \begin{array} { r r } - 3 & - 7 \ 6 & 25 \end{array} \right]$
D)
$\left[ \begin{array} { r r r } 3 & - 6 & 0 \ 0 & 0 & 25 \end{array} \right]$

Question

Find the product AB, if possible.
-$$A = \left[ \begin{array} { r r r } 
1 & 3 & - 2 \
2 & 0 & 5
\end{array} \right] , B = \left[ \begin{array} { r r } 
3 & 0 \
- 2 & 1 \
0 & 5
\end{array} \right]$$
A)
$\left[ \begin{array} { r r } - 7 & - 3 \ 25 & 6 \end{array} \right]$
B) $\mathrm { AB }$ is not defined.
C)
$\left[ \begin{array} { r r } - 3 & - 7 \ 6 & 25 \end{array} \right]$
D)
$\left[ \begin{array} { r r r } 3 & - 6 & 0 \ 0 & 0 & 25 \end{array} \right]$

Quizplus · Accepted Answer

To find the product $AB$, we multiply each row of matrix $A$ by each column of matrix $B$. For the first row of $A$ and the first column of $B$, we have $1*3 + 3*(-2) + (-2)*0 = 3 - 6 + 0 = -3$. For the first row of $A$ and the second column of $B$, we have $1*0 + 3*1 + (-2)*5 = 0 + 3 - 10 = -7$. For the second row of $A$ and the first column of $B$, we have $2*3 + 0*(-2) + 5*0 = 6 + 0 + 0 = 6$. For the second row of $A$ and the second column of $B$, we have $2*0 + 0*1 + 5*5 = 0 + 0 + 25 = 25$. Thus, the product $AB$ is $\left[ \begin{array} { r r } -3 & -7 \ 6 & 25 \end{array} \right]$.

Find the Product AB, If Possible A) [−7−3256]\left[ \begin{array} { r r } - 7 & - 3 \\ 25 & 6 \end{array} \right][−725​−36​]

Find the Product AB, If Possible A) $\left[ \begin{array} { r r } - 7 & - 3 \\ 25 & 6 \end{array} \right]$