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3 and 4 .Determinants and Matrices
easy
$\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&{{\omega ^2}}&\omega \\1&\omega &{{\omega ^2}}\end{array}\,} \right| = $
A
$3\sqrt 3 i$
B
$ - 3\sqrt 3 i$
C
$i\sqrt 3 $
D
$3$
Solution
(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$.
Standard 12
Mathematics
