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DETERMINANTS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDETERMINANTS1 Mark
Question
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 Aij is cofactors of aij, then value of $\triangle$ is given by:
  1. a11A31 + a12A32 + a13A33
  2. a11A11 + a12A21 + a13A31
  3. a21A11 + a22A12 + a23A13
  4. a11A11 + a21A21 + a31A31
✓

Answer

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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