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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
$\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&{{\omega ^2}}&\omega \\1&\omega &{{\omega ^2}}\end{array}\,} \right| = $
  • ✓
    $3\sqrt 3 i$
  • B
    $ - 3\sqrt 3 i$
  • C
    $i\sqrt 3 $
  • D
    $3$
✓

Answer

Correct option: A.
$3\sqrt 3 i$
a
(a) $\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&{{\omega ^2}}&\omega \\1&\omega &{{\omega ^2}}\end{array}\,} \right|\, = 3(\omega - {\omega ^2})$

$ = 3\,\left[ {\frac{{ - 1 + \sqrt 3 i}}{2} - \frac{{ - 1 - \sqrt 3 i}}{2}} \right] = 3\sqrt 3 \,i$.

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