Given $A = \left[ \begin{array} { l l }
0 & 5
\end{array} \right]$ , $B = \left[ \begin{array} { l l }
- 1 & 5 \
- 2 & 3
\end{array} \right]$, $C = \left[ \begin{array} { l }
1 \
5 \
0
\end{array} \right]$, $D = \left[ \begin{array} { l l l }
0 & 1 & 2 \
6 & 2 & 3
\end{array} \right]$, find $( A B ) \cdot ( C D )$

A) $190$
B) $150$
C) $45$
D) $- 150$
E) The operation cannot be performed

Question

Given $A = \left[ \begin{array} { l l } 
0 & 5
\end{array} \right]$ , $B = \left[ \begin{array} { l l } 
- 1 & 5 \
- 2 & 3
\end{array} \right]$, $C = \left[ \begin{array} { l } 
1 \
5 \
0
\end{array} \right]$, $D = \left[ \begin{array} { l l l } 
0 & 1 & 2 \
6 & 2 & 3
\end{array} \right]$, find $( A B ) \cdot ( C D )$

A) $190$
B) $150$
C) $45$
D) $- 150$
E) The operation cannot be performed

Quizplus · Accepted Answer

In order to perform the matrix multiplication $( AB ) \cdot ( CD )$, the number of columns of $AB$ must be equal to the number of rows of $CD$. However, in this case, the number of columns of $AB$ is 2 and the number of rows of $CD$ is 3, so the operation cannot be performed. Therefore, the answer is E (the operation cannot be performed).

Given A=[05]A = \left[ \begin{array} { l l } 0 & 5\end{array} \right]A=[0​5​]

Given $A = \left[ \begin{array} { l l } 0 & 5\end{array} \right]$