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Matrices and Determinants question

2011 · Shift 1 · Q44

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JEE Advanced
Mathematics
Matrices and Determinants
2011 · Shift 1 · Q44

Matrices and Determinants question

2011 · Shift 1 · Q44

JEE AdvancedMathematicsMatrices and DeterminantsMCQ+3 / −1

Let a, b and c be three real numbers satisfying

[\begin{matrix} a & b & c \\ \end{matrix} ]\left[ {\begin{matrix} 1 & 9 & 7 \\ 8 & 2 & 7 \\ 7 & 3 & 7 \\ \end{matrix} } \right] = [\begin{matrix} 0 & 0 & 0 \\ \end{matrix} ]

........(E)Let

\omega

be a solution of

{x^3} - 1 = 0

with

{\mathop{\rm Im} olimits} (\omega ) \gt 0

. If a = 2 with b and c satisfying (E), then the value of

{3 \over {{\omega ^a}}} + {1 \over {{\omega ^b}}} + {3 \over {{\omega ^c}}}

is equal to

A
$-$ 2
B
2
C
3
D
$-$ 3

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