a, b, c are non-zero real numbers. Then | array lll c & a & ~b a & ~b & ~b ~b & ~b & a…
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
a, b, c are non-zero real numbers. Then
\[\left|\begin{array}{lll} \mathrm{c} & \mathrm{a} & \mathrm{~b} \\ \mathrm{a} & \mathrm{~b} & \mathrm{~b} \\ \mathrm{~b} & \mathrm{~b} & \mathrm{a} \end{array}\right|\] = 0, if
\[\left|\begin{array}{lll} \mathrm{c} & \mathrm{a} & \mathrm{~b} \\ \mathrm{a} & \mathrm{~b} & \mathrm{~b} \\ \mathrm{~b} & \mathrm{~b} & \mathrm{a} \end{array}\right|\] = 0, if
- \(\frac{1}{a}+\frac{1}{b \omega}+\frac{1}{c \omega^{2}}=0\)
- \(\frac{1}{\mathrm{a}}+\frac{1}{\mathrm{~b} \omega^{2}}+\frac{1}{\mathrm{c} \omega}=0\)
- \(\frac{1}{a \omega}+\frac{1}{b \omega^{2}}+\frac{1}{c}=0\)
- none of these
Answer
(A) 1 a + 1 b + 1 c ^ 2 =0, (B) 1 a + 1 ~b ^ 2 + 1 c =0, (C) 1 a + 1 b ^ 2 + 1 c =0
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