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Q.

Let $Δ = |\begin{array}{lll} 1 a a^{2} - b c \\ 1 b b^{2} - c a \\ 1 c c^{2} - a b \end{array}|$ , then $∆$ is equal to

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a

none of these

b

0

c

$\frac{1}{2} (a^{2} + b^{2} + c^{2})$

d

$a + b + c$

answer is A.

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Detailed Solution

Applying $R_{2} \to R_{2} - R_{1} + R_{3} \to R_{3} - R_{1}$ we get

$Δ = (b - a) (c - a) |\begin{array}{lll} 1 a a^{2} - b c \\ 0 1 a + b + c \\ 0 1 a + b + c \end{array}| = 0$

$[∵ R_{2} and R_{3} are identical]$

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