If \( A=[a_{ij}]_{3\times 3}=\begin{bmatrix}2 & 3 & -1\\1 & 2 & 3\\0 & -1 & 1\end{bmatrix} \) and \( B=[b_{ij}]_{3\times 2}=\begin{bmatrix}3 & -2\\1 & 4\\1 & 2\end{bmatrix} \) then the value of \( a_{12}b_{21}+a_{32}b_{31} \) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 2
In \( a_{ij} \), i is the row and j is the column.
\( \displaystyle a_{12}=3\ \text{(row 1, column 2)} \)
\( \displaystyle a_{32}=-1\ \text{(row 3, column 2)} \)
\( \displaystyle b_{21}=1\ \text{(row 2, column 1)} \)
\( \displaystyle b_{31}=1\ \text{(row 3, column 1)} \)
\( \displaystyle a_{12}b_{21}+a_{32}b_{31}=3(1)+(-1)(1) \)
\( \displaystyle =3-1=2 \)