JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(\omega \) be a complex number such that \(2\omega + 1 = z\) where \(z = \sqrt { - 3} \) . If \(\left| {\begin{array}{*{20}{c}}1&1&1\\1&{ - {\omega ^2} - 1}&{{\omega ^2}}\\1&{{\omega ^2}}&{{\omega ^7}}\end{array}} \right| = 3k\) then \(k\) is equal to :
- A \(1\)
- B \(-z\)
- C \(z\)
- D \(-1\)
Answer & Solution
Correct Answer
(B) \(-z\)
Step-by-step Solution
Detailed explanation
Given \(2\omega + 1 = z;\) \(z = \sqrt {3i} \) \( \Rightarrow \omega = \frac{{\sqrt {3i} - 1}}{2}\) \( \Rightarrow \omega \) is complex cube root of unity Applying \({R_1} \to {R_1} + {R_2} + {R_3}\)…
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