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3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
$\Delta = \left| {\,\begin{array}{*{20}{c}}a&{a + b}&{a + b + c}\\{3a}&{4a + 3b}&{5a + 4b + 3c}\\{6a}&{9a + 6b}&{11a + 9b + 6c}\end{array}\,} \right|$where $a = i,b = \omega ,c = {\omega ^2}$, then $\Delta $is equal to
  • ✓
    $i$
  • B
    $ - {\omega ^2}$
  • C
    $\omega $
  • D
    $ - i$
✓

Answer

Correct option: A.
$i$
a
(a) We first operating ${R_3} - 2{R_2}$ and ${R_2} - 3{R_1}$ in given determinant, then we get

$ = a[{a^2} + ab - 2{a^2} - ab] = - {a^3} = i$.

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