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Matrices and Determinants

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Let a, b and c be three real numbers satisfying

\begin{bmatrix} a & b & c \end{bmatrix} \begin{bmatrix} 1 & 9 & 7 \\ 8 & 2 & 7 \\ 7 & 3 & 7 \end{bmatrix}

=

\begin{bmatrix} 0 & 0 & 0 \end{bmatrix}

(E)

Section: Mathematics

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Question : 46 of 56

Marks: +1, -0

Let ω be a solution of

x^3 - 1

= 0 with Im(ω) > 0. If a = 2 with b and c satisfying (E), then the value of

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

[JEE Adv 2011 P1]

−2
2
3
−3

Solution:

Here, a = 2, b and c satisfies (E); b = 12, c = − 14.

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

=

\frac{1}{\omega^2} + \frac{1}{\omega^{12}} + \frac{3}{\omega^{-14}}

= - 2

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