If a- b- c are three complex numbers such that a2-b2-c2-0 and beginvmatrix b- 2-c- 2 - a b - a ca b -c- 2-a- 2 - b ca c - b c -a- 2-b- 2lend vmatrix - K - a - 2 b - 2 c - 2 V then K is -A- 1B- 2C- -2D- 4

The correct option is D 4= a^2 amp; ab amp; ac nbsp; ab amp; b^2 amp; bc nbsp; ac amp; bc amp; c^2 =abc a amp; a amp; a n ...

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Evaluation of a Determinant

If a, b, c ar...

Question

If $a, b, c$ are three complex numbers such that $a^{2} + b^{2} + c^{2} = 0$ and
$∣ ∣ ∣ ∣ ∣ \begin{matrix} (b^{2} + c^{2}) & a b & a c a b & (c^{2} + a^{2}) & b c a c & b c & (a^{2} + b^{2}) \end{matrix} ∣ ∣ ∣ ∣ ∣ = K a^{2} b^{2} c^{2}$ then $K$ is -

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a, b, c

a^{2} + b^{2} + c^{2} = 0

∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} + c^{2} & a b & a c a b & c^{2} + a^{2} & b c a c & b c & a^{2} + b^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ = k a^{2} b^{2} c^{2}

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∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} + c^{2} & a b & a c a b & c^{2} + a^{2} & b c c a & c b & a^{2} + b^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ = k a^{2} b^{2} c^{2},

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a, b, c

a^{2} + b^{2} + c^{2} = 0

Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} + c^{2} & a b & a c a b & c^{2} + a^{2} & b c a c & b c & a^{2} + b^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ = k a^{2} b^{2} c^{2}

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