Find the matrix product AB, if it is defined.
-$$A = \left[ \begin{array} { r r }
- 1 & 3 \
1 & 6
\end{array} \right] , B = \left[ \begin{array} { l l l }
0 & - 2 & 6 \
1 & - 3 & 2
\end{array} \right]$$
A) $\mathrm { AB }$ is undefined.
B)
$$\left[ \begin{array} { r r }
0 & - 6 \
18 & 1 \
- 18 & 12
\end{array} \right]$$
C)
$$\left[ \begin{array} { r r r }
3 & 6 & - 7 \
- 20 & 0 & 18
\end{array} \right]$$
D)
$$\left[ \begin{array} { r r r }
3 & - 7 & 0 \
6 & - 20 & 18
\end{array} \right]$$

Question

Find the matrix product AB, if it is defined.
-$$A = \left[ \begin{array} { r r } 
- 1 & 3 \
1 & 6
\end{array} \right] , B = \left[ \begin{array} { l l l } 
0 & - 2 & 6 \
1 & - 3 & 2
\end{array} \right]$$
A) $\mathrm { AB }$ is undefined.
B)
$$\left[ \begin{array} { r r } 
0 & - 6 \
18 & 1 \
- 18 & 12
\end{array} \right]$$
C)
$$\left[ \begin{array} { r r r } 
3 & 6 & - 7 \
- 20 & 0 & 18
\end{array} \right]$$
D)
$$\left[ \begin{array} { r r r } 
3 & - 7 & 0 \
6 & - 20 & 18
\end{array} \right]$$

Quizplus · Accepted Answer

The product of matrices A and B is calculated by multiplying rows of A by columns of B. For AB, the resulting matrix is:$$AB = \left[ \begin{array}{cc} -1*0 + 3*1 & -1*(-2) + 3*(-3) & -1*6 + 3*2 \1*0 + 6*1 & 1*(-2) + 6*(-3) & 1*6 + 6*2\end{array} \right] = \left[ \begin{array}{ccc} 3 & -7 & 0 \6 & -20 & 18\end{array} \right]$$

Find the Matrix Product AB, If It Is Defined A) AB\mathrm { AB }AB

Find the Matrix Product AB, If It Is Defined A) $\mathrm { AB }$