If A= a_ 11 &a_ 12 &a_ 13 _ 21 &a_ 22 &a_ 23 _ 31 &a_ 32 &a_ 33 a… - Vidyadip

MCQ

If $\text{A}=\begin{vmatrix}\text{a}_{11}&\text{a}_{12}&\text{a}_{13}\\\text{a}_{21}&\text{a}_{22}&\text{a}_{23}\\\text{a}_{31}&\text{a}_{32}&\text{a}_{33}\end{vmatrix}$ and $C_\text{ij}$ is cofactor of $a_\text{ij}$ in $a$, then value of $|A|$ is given by:

A
$a_{11} C_{31}+a_{12} C_{32}+a_{13} C_{33}$
B
$a_{11} C_{11}+a_{12} C_{21}+a_{13} C_{31}$
C
$a_{21} C_{11}+a_{22} C_{12}+a_{23} C_{13}$
✓
$a_{11} C_{11}+a_{21} C_{21}+a_{13} C_{31}$

✓

Answer

Correct option: D.

$a_{11} C_{11}+a_{21} C_{21}+a_{13} C_{31}$

Properties of determinants state that if a is a square matrix of the order $n,$ then Det $(A)$ is the sum of products of elements of a row $($or a column$)$ with the
corresponding cofactor of that element.

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