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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
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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