MCQ
If $\triangle=\begin{vmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{vmatrix}$ and $A_{ji}$ is cofactors of $a_{ji}$, then value of $\triangle$ 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
    $a_{21} A_{11}+a_{22} A_{12}+a_{23} A_{13}$
  • $a_{11} A_{11}+a_{21} A_{21}+a_{31} A_{31}$

Answer

Correct option: D.
$a_{11} A_{11}+a_{21} A_{21}+a_{31} A_{31}$
We know that: $\triangle$ = Sum of the product of the elements of a column (or a row) with their corresponding cofactors $\therefore\triangle = \text{a}_{11}\text{A}_{11} +\text{a}_{21}\text{A}_{21} + \text{a}_{31}\text{A}_{31}$ Hence, the value of $\triangle$ is given by the expression given in alternative d. the correct answer is d.

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