If $A = ⎡ ⎢ ⎣ \begin{matrix} 3 & 2 & 4 1 & 2 & 1 3 & 2 & 6 \end{matrix} ⎤ ⎥ ⎦$ and $A_{i j}$ are the cofactors of $a_{i j}$ , then $a_{11} A_{11} + a_{12} A_{12} + a_{13} A_{13}$ is equal to

8

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

6

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $8$
$a_{11} A_{11} + a_{12} A_{12} + A_{13} A_{13}$
$= 3 ∣ ∣ ∣ \begin{matrix} 2 & 1 2 & 6 \end{matrix} ∣ ∣ ∣ - 2 ∣ ∣ ∣ \begin{matrix} 1 & 1 3 & 6 \end{matrix} ∣ ∣ ∣ + 4 ∣ ∣ ∣ \begin{matrix} 1 & 2 3 & 2 \end{matrix} ∣ ∣ ∣$
$= 3 (12 - 2) - 2 (6 - 3) + 4 (2 - 6)$
$= 30 - 6 - 16$
$= 8$

Suggest Corrections

Similar questions

If $Δ ∣ ∣ ∣ ∣ \begin{matrix} a_{11} & a_{12} & a_{13} a_{21} & a_{22} & a_{23} a_{31} & a_{32} & a_{33} \end{matrix} ∣ ∣ ∣ ∣$ and $A_{i j}$ is cofactor of $a_{i j}$ , then value of $Δ$ is given by

a) $a_{11} A_{31} + a_{12} A_{32} + a_{13} A_{33}$
b) $a_{11} A_{11} + a_{12} A_{21} + a_{13} A_{31}$
c) $a_{21} A_{11} + a_{22} A_{12} + a_{23} A_{13}$
d) $a_{11} A_{11} + a_{21} A_{21} + a_{31} A_{31}$