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3 and 4 .Determinants and Matrices
medium
જો $\omega $ એ એકનું કાલ્પનિક બીજ હોય , તો $\left| {\,\begin{array}{*{20}{c}}1&\omega &{ - {\omega ^2}/2}\\1&1&1\\1&{ - 1}&0\end{array}\,} \right| = $
A
$0$
B
$1$
C
$\omega $
D
${\omega ^2}$
Solution
(a) $\left| {\,\begin{array}{*{20}{c}}1&\omega &{ – {\omega ^2}/2}\\1&1&1\\1&{ – 1}&0\end{array}\,} \right| = – \frac{1}{2}\left| {\,\begin{array}{*{20}{c}}1&\omega &{{\omega ^2}}\\1&1&{ – 2}\\1&{ – 1}&0\end{array}\,} \right|$
= $ – \frac{1}{2}\left| {\,\begin{array}{*{20}{c}}0&\omega &{{\omega ^2}}\\0&1&{ – 2}\\0&{ – 1}&0\end{array}\,} \right| = 0$, (Apply ${C_1} \to {C_1} + {C_2} + {C_3})$.
Standard 12
Mathematics
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